Design Deliverables and Engineering Review

Design objective: Create traceable, reviewable handover documents that preserve uncertainty and distinguish conceptual from detailed design.

Common teaching scenario: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.

Unit-level engineering decision

The essential problem in this unit is not memorizing equations. It is forming a defensible decision from incomplete evidence. Create traceable, reviewable handover documents that preserve uncertainty and distinguish conceptual from detailed design. The case studies are synthetic; they provide a transparent set of inputs that can be checked without access to an operating facility. Before a numerical conclusion is adopted, identify the required physical evidence, constraints, and operating modes. Make clear whether the outcome is a conceptual screening result, a preliminary design basis, a vendor-specified rating, or a compliance decision. The four lessons examine distinct aspects of this decision.

Structured lesson sequence

1. [Process flow diagrams and stream tables](../lessons/unit-08-lesson-01.html)

PFDs should make equipment sequence and principal mass-energy quantities auditable. Governing equation: component residual = Σ component input − Σ component output. Numerical benchmark: Two inlet streams each 5 t/h, with 10% and 30% target component, yield 2 t/h component at a nonreacting outlet. Decision question: Use a unit-boundary stream register and independent residual checks before reviewing details.

2. [Instrumentation and P&ID design intent](../lessons/unit-08-lesson-02.html)

P&IDs communicate controls and process connections that a high-level PFD omits. Governing equation: tag traceability = equipment/line/instrument identifier linked to an approved source. Numerical benchmark: A controlled valve tag can identify a proposed manipulated variable; its fail action needs a hazard-based decision. Decision question: Check that every functional claim is supported by a separate instrument/control document.

3. [Design audit, traceability and unresolved actions](../lessons/unit-08-lesson-03.html)

A project handover is incomplete when critical assumptions lack owners or test evidence. Governing equation: unresolved fraction = open high-priority items / total high-priority items. Numerical benchmark: If 3 of 12 critical decisions remain open, 25% are unresolved; progress counts do not measure their severity. Decision question: Separate deliverables that exist from decisions that are technically verified.

4. [Final project decision and uncertainty communication](../lessons/unit-08-lesson-04.html)

Integrate transparent economics and engineering risk without false numeric certainty. Governing equation: decision case = base forecast + downside and upside stress cases. Numerical benchmark: If costs are uncertain by 20% and annual contribution by 15%, both should be varied with consistent cash-flow logic. Decision question: Write an evidence-triggered go/no-go memo listing remaining tests, owners and cost to obtain missing information.

Integrated design activity

Construct a compact design dossier for the following system: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log. The dossier must contain a flowsheet or decision diagram, a variable and unit register, an assumption register, at least two checks based on first principles, a sensitivity chart from one of the interactive models, a documented failure case, and an explicit decision with a reversal condition. Begin with the minimum information needed to formulate the problem; do not assign invented precise values to unknown vendor or market inputs. When data is unavailable, use a marked synthetic scenario and report the evidence gap.

Evidence and model boundaries

Topic 1 — Process flow diagrams and stream tables. No stream table should claim numerical closure without the basis and units. The next evidence sources are flow measurements, equipment schedule, property package and process data. Any screening estimate using component residual = Σ component input − Σ component output remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Topic 2 — Instrumentation and P&ID design intent. ISO 10628 describes flow-diagram specifications, not an automatic safety approval for P&IDs. The next evidence sources are instrument index, control philosophy, trip cause-effect matrix and operations review. Any screening estimate using tag traceability = equipment/line/instrument identifier linked to an approved source remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Topic 3 — Design audit, traceability and unresolved actions. Critical hold points cannot be averaged away with many harmless closed items. The next evidence sources are issue tracker, owners, due dates, evidence file and approval signatures. Any screening estimate using unresolved fraction = open high-priority items / total high-priority items remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Topic 4 — Final project decision and uncertainty communication. Use a seed-fixed distribution to demonstrate numerical method, not likelihood of real plant success. The next evidence sources are auditable cost estimates, demand contracts, pilot yields and approvals. Any screening estimate using decision case = base forecast + downside and upside stress cases remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Unit laboratories

• [Lab 22: Design-basis change traceability](../labs/lab-22.html) — Explore a numerical checklist without pretending it is safety certification.. Verification: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added.

• [Lab 23: PFD stream-table conservation audit](../labs/lab-23.html) — Expose component residual when an assumed product composition conflicts with feed measurements.. Verification: For chosen base data, x_out=0.2 gives zero component residual.

• [Lab 24: Scenario uncertainty and project NPV](../labs/lab-24.html) — Demonstrate that a distribution of spreadsheet inputs does not constitute measured project risk.. Verification: At zero scenario span, every simulated NPV must equal the same deterministic value.

Unit review protocol

For each model, run default and altered cases. Check the governing relation algebraically for one point; verify dimensional consistency and domain validity; identify at least one limiting case; export a CSV and preserve the selected parameter settings in the report. A smooth graph can still be wrong, so treat independent calculations and physical evidence as separate gates. Before using the result outside a classroom, request suitable measured inputs, professional design reviews and applicable approvals.

[16-question assessment](../assessments/unit-08.html) · [Applied project](../projects/unit-08.html) · [Book contents](../index.html)

Unit 8 · Lesson 1: Process flow diagrams and stream tables

Learning pathway: [Design Deliverables and Engineering Review](../units/unit-08.html) · [Simulation 23: PFD stream-table conservation audit](../labs/lab-23.html) · [Assessment](../assessments/unit-08.html).

Engineering problem and conceptual boundary

PFDs should make equipment sequence and principal mass-energy quantities auditable. The central design case for this part of the course is: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Use a unit-boundary stream register and independent residual checks before reviewing details.

A PFD is not a piping and instrumentation diagram; instrument details and safeguards need separate documents. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is component residual = Σ component input − Σ component output. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For process flow diagrams and stream tables, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: No stream table should claim numerical closure without the basis and units. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: Two inlet streams each 5 t/h, with 10% and 30% target component, yield 2 t/h component at a nonreacting outlet. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for process flow diagrams and stream tables but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 23: PFD stream-table conservation audit](../labs/lab-23.html). The implemented relation is Residual A = (F1 x1 + F2 x2) − (F1+F2)x_out. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: For chosen base data, x_out=0.2 gives zero component residual. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Deliberately enter an inconsistent outlet composition and quantify the component-closure error. The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: flow measurements, equipment schedule, property package and process data. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Use a unit-boundary stream register and independent residual checks before reviewing details. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: No stream table should claim numerical closure without the basis and units. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: flow measurements, equipment schedule, property package and process data Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: Nonreactive mixer; neglects unmeasured outlets, reaction, accumulation and phase change. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for process flow diagrams and stream tables lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: flow measurements, equipment schedule, property package and process data. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation component residual = Σ component input − Σ component output is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Process flow diagrams and stream tables.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: No stream table should claim numerical closure without the basis and units.
• I can run and explain the numerical limit test: For chosen base data, x_out=0.2 gives zero component residual.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: flow measurements, equipment schedule, property package and process data

[Unit 8 overview](../units/unit-08.html) · [Lab 23](../labs/lab-23.html) · [Unit 8 assessment](../assessments/unit-08.html) · [Book contents](../index.html)

Unit 8 · Lesson 2: Instrumentation and P&ID design intent

Learning pathway: [Design Deliverables and Engineering Review](../units/unit-08.html) · [Simulation 22: Design-basis change traceability](../labs/lab-22.html) · [Assessment](../assessments/unit-08.html).

Engineering problem and conceptual boundary

P&IDs communicate controls and process connections that a high-level PFD omits. The central design case for this part of the course is: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Check that every functional claim is supported by a separate instrument/control document.

An icon or tag name does not prove that relief, interlocks or alarms are correct. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is tag traceability = equipment/line/instrument identifier linked to an approved source. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For instrumentation and p&id design intent, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: ISO 10628 describes flow-diagram specifications, not an automatic safety approval for P&IDs. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: A controlled valve tag can identify a proposed manipulated variable; its fail action needs a hazard-based decision. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for instrumentation and p&id design intent but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 22: Design-basis change traceability](../labs/lab-22.html). The implemented relation is Closure fraction = verified, approved requirements / all critical requirements. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Explain why closing ten low-criticality items cannot override an open high-severity hazard review. The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: instrument index, control philosophy, trip cause-effect matrix and operations review. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Check that every functional claim is supported by a separate instrument/control document. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: ISO 10628 describes flow-diagram specifications, not an automatic safety approval for P&IDs. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: instrument index, control philosophy, trip cause-effect matrix and operations review Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: An issue-counting dashboard is not proof of safety or quality; critical hold points remain mandatory. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for instrumentation and p&id design intent lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: instrument index, control philosophy, trip cause-effect matrix and operations review. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation tag traceability = equipment/line/instrument identifier linked to an approved source is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Instrumentation and P&ID design intent.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: ISO 10628 describes flow-diagram specifications, not an automatic safety approval for P&IDs.
• I can run and explain the numerical limit test: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: instrument index, control philosophy, trip cause-effect matrix and operations review

[Unit 8 overview](../units/unit-08.html) · [Lab 22](../labs/lab-22.html) · [Unit 8 assessment](../assessments/unit-08.html) · [Book contents](../index.html)

Unit 8 · Lesson 3: Design audit, traceability and unresolved actions

Learning pathway: [Design Deliverables and Engineering Review](../units/unit-08.html) · [Simulation 22: Design-basis change traceability](../labs/lab-22.html) · [Assessment](../assessments/unit-08.html).

Engineering problem and conceptual boundary

A project handover is incomplete when critical assumptions lack owners or test evidence. The central design case for this part of the course is: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Separate deliverables that exist from decisions that are technically verified.

Completeness scores can reward paperwork while leaving material hazards unresolved. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is unresolved fraction = open high-priority items / total high-priority items. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For design audit, traceability and unresolved actions, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: Critical hold points cannot be averaged away with many harmless closed items. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: If 3 of 12 critical decisions remain open, 25% are unresolved; progress counts do not measure their severity. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for design audit, traceability and unresolved actions but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 22: Design-basis change traceability](../labs/lab-22.html). The implemented relation is Closure fraction = verified, approved requirements / all critical requirements. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Explain why closing ten low-criticality items cannot override an open high-severity hazard review. The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: issue tracker, owners, due dates, evidence file and approval signatures. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Separate deliverables that exist from decisions that are technically verified. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: Critical hold points cannot be averaged away with many harmless closed items. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: issue tracker, owners, due dates, evidence file and approval signatures Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: An issue-counting dashboard is not proof of safety or quality; critical hold points remain mandatory. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for design audit, traceability and unresolved actions lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: issue tracker, owners, due dates, evidence file and approval signatures. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation unresolved fraction = open high-priority items / total high-priority items is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Design audit, traceability and unresolved actions.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: Critical hold points cannot be averaged away with many harmless closed items.
• I can run and explain the numerical limit test: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: issue tracker, owners, due dates, evidence file and approval signatures

[Unit 8 overview](../units/unit-08.html) · [Lab 22](../labs/lab-22.html) · [Unit 8 assessment](../assessments/unit-08.html) · [Book contents](../index.html)

Unit 8 · Lesson 4: Final project decision and uncertainty communication

Learning pathway: [Design Deliverables and Engineering Review](../units/unit-08.html) · [Simulation 24: Scenario uncertainty and project NPV](../labs/lab-24.html) · [Assessment](../assessments/unit-08.html).

Engineering problem and conceptual boundary

Integrate transparent economics and engineering risk without false numeric certainty. The central design case for this part of the course is: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Write an evidence-triggered go/no-go memo listing remaining tests, owners and cost to obtain missing information.

A probability distribution is only as valid as its source and correlation assumptions. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is decision case = base forecast + downside and upside stress cases. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For final project decision and uncertainty communication, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: Use a seed-fixed distribution to demonstrate numerical method, not likelihood of real plant success. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: If costs are uncertain by 20% and annual contribution by 15%, both should be varied with consistent cash-flow logic. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for final project decision and uncertainty communication but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 24: Scenario uncertainty and project NPV](../labs/lab-24.html). The implemented relation is NPV = −I + annual net CF × annuity factor; input uncertainty via seeded triangular draws. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: At zero scenario span, every simulated NPV must equal the same deterministic value. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Compare negative-NPV share under two assumed spans; explain why these are scenario outcomes, not forecasts. The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: auditable cost estimates, demand contracts, pilot yields and approvals. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Write an evidence-triggered go/no-go memo listing remaining tests, owners and cost to obtain missing information. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: Use a seed-fixed distribution to demonstrate numerical method, not likelihood of real plant success. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: auditable cost estimates, demand contracts, pilot yields and approvals Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: Independently seeded synthetic triangular changes for investment/cash flow; fixed six-year horizon and no real probability calibration. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for final project decision and uncertainty communication lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: auditable cost estimates, demand contracts, pilot yields and approvals. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation decision case = base forecast + downside and upside stress cases is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Final project decision and uncertainty communication.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: Use a seed-fixed distribution to demonstrate numerical method, not likelihood of real plant success.
• I can run and explain the numerical limit test: At zero scenario span, every simulated NPV must equal the same deterministic value.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: auditable cost estimates, demand contracts, pilot yields and approvals

[Unit 8 overview](../units/unit-08.html) · [Lab 24](../labs/lab-24.html) · [Unit 8 assessment](../assessments/unit-08.html) · [Book contents](../index.html)

Applied design project 8: Design Deliverables and Engineering Review

Scenario: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.

Engineering goal: Create traceable, reviewable handover documents that preserve uncertainty and distinguish conceptual from detailed design.

Project brief and boundary

You are a junior design team preparing a conceptual recommendation for a supervised technical review. The project is not a request to produce construction-ready specifications. It asks whether a candidate concept merits a funded next study based on traceable evidence. Make one primary design decision linked to design deliverables and engineering review and identify both how it could fail and what information is needed before capital is committed. Design responsibility, commercial feasibility, safety, permit requirements and site-specific code compliance remain independent gate reviews.

Task A — Form a reproducible design basis

A1. Process flow diagrams and stream tables: PFDs should make equipment sequence and principal mass-energy quantities auditable. Start from component residual = Σ component input − Σ component output and reproduce the benchmark: Two inlet streams each 5 t/h, with 10% and 30% target component, yield 2 t/h component at a nonreacting outlet. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: flow measurements, equipment schedule, property package and process data.

A2. Instrumentation and P&ID design intent: P&IDs communicate controls and process connections that a high-level PFD omits. Start from tag traceability = equipment/line/instrument identifier linked to an approved source and reproduce the benchmark: A controlled valve tag can identify a proposed manipulated variable; its fail action needs a hazard-based decision. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: instrument index, control philosophy, trip cause-effect matrix and operations review.

A3. Design audit, traceability and unresolved actions: A project handover is incomplete when critical assumptions lack owners or test evidence. Start from unresolved fraction = open high-priority items / total high-priority items and reproduce the benchmark: If 3 of 12 critical decisions remain open, 25% are unresolved; progress counts do not measure their severity. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: issue tracker, owners, due dates, evidence file and approval signatures.

A4. Final project decision and uncertainty communication: Integrate transparent economics and engineering risk without false numeric certainty. Start from decision case = base forecast + downside and upside stress cases and reproduce the benchmark: If costs are uncertain by 20% and annual contribution by 15%, both should be varied with consistent cash-flow logic. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: auditable cost estimates, demand contracts, pilot yields and approvals.

Task B — Build a traceable numerical investigation

[Lab 22 — Design-basis change traceability](../labs/lab-22.html): Explain why closing ten low-criticality items cannot override an open high-severity hazard review. Validate the bound: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added. Export the CSV and annotate which equation limits the model. Do not claim that an illustrative spreadsheet predicts a real plant.

[Lab 23 — PFD stream-table conservation audit](../labs/lab-23.html): Deliberately enter an inconsistent outlet composition and quantify the component-closure error. Validate the bound: For chosen base data, x_out=0.2 gives zero component residual. Export the CSV and annotate which equation limits the model. Do not claim that an illustrative spreadsheet predicts a real plant.

[Lab 24 — Scenario uncertainty and project NPV](../labs/lab-24.html): Compare negative-NPV share under two assumed spans; explain why these are scenario outcomes, not forecasts. Validate the bound: At zero scenario span, every simulated NPV must equal the same deterministic value. Export the CSV and annotate which equation limits the model. Do not claim that an illustrative spreadsheet predicts a real plant.

Task C — Challenge the concept

Construct a short failure-first register with at least one physical failure, one commercial or cost failure, one operational difficulty and one missing-data risk. For design deliverables and engineering review, list the observable sign of each problem, the assumption it challenges and the cheapest credible test that could expose it. A risk register without an assigned next action or a stop/go criterion is not a useful project deliverable. Distinguish a design variation from an independent protection measure and seek qualified safety review where warranted.

Task D — Submit an engineering decision pack

The pack contains: (1) design-basis sheet; (2) flowsheet or concept comparison; (3) numbered stream and parameter tables with units; (4) independent hand checks; (5) controlled simulation figures and exported CSV; (6) constraints and exclusions; (7) cost or utility sensitivity where relevant; (8) failure and uncertainty register; (9) recommendation with what evidence would reverse it; (10) references and revision log. Document whether assumptions are invented for pedagogy, grounded in a published reference, requested from a supplier, or measured. A professionally reviewed design would need additional engineering discipline sign-offs.

Acceptance test

A reviewer unfamiliar with your work should be able to reproduce a benchmark from the unit, locate the 3 related labs, see why the governing equations are dimensionally consistent, find at least one intentionally adverse case, and identify an unresolved assumption that could invalidate the proposed decision. The case is: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log. All evidence obtained and not obtained should be distinguishable. Do not present an unresolved conceptual model as an approved site or plant design.

[Unit notes](../units/unit-08.html) · [Unit assessment](../assessments/unit-08.html)

Unit 8 assessment — Design Deliverables and Engineering Review

Context: A hypothetical capital-review dossier, including a basis of design, PFD, equipment list, assumptions, safety gaps and revision log.

Answer all sixteen multi-part problems. All illustrative figures are synthetic. Include units, inputs, methods, checking and limitations. Each problem should use a different numerical or investigative test; do not replace a requested calculation with a qualitative assertion.

Multi-part questions

Lesson 1: Process flow diagrams and stream tables

Q1 — First-principles reconstruction. Starting with the physical boundary discussed in Process flow diagrams and stream tables, derive or justify component residual = Σ component input − Σ component output in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: Two inlet streams each 5 t/h, with 10% and 30% target component, yield 2 t/h component at a nonreacting outlet. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q2 — Perturbation study. In [Lab 23](../labs/lab-23.html), take the baseline parameter set, vary Claimed outlet mass fraction through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q3 — Independent falsification. Test the assertion: For chosen base data, x_out=0.2 gives zero component residual. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q4 — Evidence and decision memo. Write a 200–300-word decision note addressing: Use a unit-boundary stream register and independent residual checks before reviewing details. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: flow measurements, equipment schedule, property package and process data. Discuss this known limitation: No stream table should claim numerical closure without the basis and units. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Lesson 2: Instrumentation and P&ID design intent

Q5 — First-principles reconstruction. Starting with the physical boundary discussed in Instrumentation and P&ID design intent, derive or justify tag traceability = equipment/line/instrument identifier linked to an approved source in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: A controlled valve tag can identify a proposed manipulated variable; its fail action needs a hazard-based decision. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q6 — Perturbation study. In [Lab 22](../labs/lab-22.html), take the baseline parameter set, vary Verified critical requirements through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q7 — Independent falsification. Test the assertion: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q8 — Evidence and decision memo. Write a 200–300-word decision note addressing: Check that every functional claim is supported by a separate instrument/control document. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: instrument index, control philosophy, trip cause-effect matrix and operations review. Discuss this known limitation: ISO 10628 describes flow-diagram specifications, not an automatic safety approval for P&IDs. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Lesson 3: Design audit, traceability and unresolved actions

Q9 — First-principles reconstruction. Starting with the physical boundary discussed in Design audit, traceability and unresolved actions, derive or justify unresolved fraction = open high-priority items / total high-priority items in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: If 3 of 12 critical decisions remain open, 25% are unresolved; progress counts do not measure their severity. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q10 — Perturbation study. In [Lab 22](../labs/lab-22.html), take the baseline parameter set, vary Verified critical requirements through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q11 — Independent falsification. Test the assertion: Closure fraction cannot exceed 100% and must decrease when unresolved requirements are added. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q12 — Evidence and decision memo. Write a 200–300-word decision note addressing: Separate deliverables that exist from decisions that are technically verified. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: issue tracker, owners, due dates, evidence file and approval signatures. Discuss this known limitation: Critical hold points cannot be averaged away with many harmless closed items. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Lesson 4: Final project decision and uncertainty communication

Q13 — First-principles reconstruction. Starting with the physical boundary discussed in Final project decision and uncertainty communication, derive or justify decision case = base forecast + downside and upside stress cases in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: If costs are uncertain by 20% and annual contribution by 15%, both should be varied with consistent cash-flow logic. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q14 — Perturbation study. In [Lab 24](../labs/lab-24.html), take the baseline parameter set, vary Baseline investment through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q15 — Independent falsification. Test the assertion: At zero scenario span, every simulated NPV must equal the same deterministic value. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q16 — Evidence and decision memo. Write a 200–300-word decision note addressing: Write an evidence-triggered go/no-go memo listing remaining tests, owners and cost to obtain missing information. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: auditable cost estimates, demand contracts, pilot yields and approvals. Discuss this known limitation: Use a seed-fixed distribution to demonstrate numerical method, not likelihood of real plant success. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Marking and evidence standards

Allocate 25% to correct model and dimensions, 25% to worked numeric results and residual checks, 25% to parameter investigation and plots, and 25% to evidence quality, limitations and communication. Submit calculations, CSV exports, a one-page design note and a clearly labeled outstanding-information list. Material that implies these synthetic results certify an industrial design should not receive full credit.

[Unit notes](../units/unit-08.html) · [Applied project](../projects/unit-08.html)