Engineering Quantities, Dimensions and Systems of Units

Central engineering problem

A numerical answer without a unit, physical basis and sensible magnitude check is not an engineering result.

The unit develops four tightly connected ideas. A process description should become a quantitative and testable claim: an explicit boundary, evidence for values, dimensional consistency, and a way to distinguish real physical behavior from model simplifications. The relevant measurements and operating envelopes must be named before making a process decision. In introductory chemical engineering, a plausible numerical result is necessary but not sufficient; it must also obey conservation, physical feasibility and operational safety.

Learning outcomes

After studying this unit, a student should be able to explain the physical role of the four topics, construct or interpret a simple numerical representation, identify a falsifying measurement, and document how the assumptions restrict the result. Numerical work should use explicit material or energy bases and show uncertainty or sensitivity whenever decisions depend on approximate data.

Lesson sequence

• [SI units and dimensional consistency](../lessons/unit-02-lesson-01.html)
• [Flow rates and concentration measures](../lessons/unit-02-lesson-02.html)
• [Properties and reference conditions](../lessons/unit-02-lesson-03.html)
• [Estimation, uncertainty and scale](../lessons/unit-02-lesson-04.html)

Interactive laboratories

• [Lab 03: Volumetric-to-mass-flow conversion](../labs/lab-03.html)
• [Lab 04: Concentration and composition in blended streams](../labs/lab-04.html)

Synthesis activity

Build a one-page process evidence sheet that distinguishes four columns: directly observed quantities, derived quantities, estimated properties, and external constraints. For each lesson's primary equation, test whether a 10% change in its dominant input yields a proportionate response. Explain exceptions, including compositions bounded between zero and one and physical states requiring feasibility checks. Conclude with at least two measurements needed to confirm the result in a real laboratory or plant.

Assessment standard

Successful work must show a system boundary or process purpose, symbolic equations before values, units during substitution, an independent conservation or limiting-case check, and a concise explanation of where a more advanced treatment is required. Attach plots only when their input assumptions are documented. The purpose is transferable engineering reasoning rather than memorized formula application.

Unit 2.1: SI units and dimensional consistency

Chemical Engineering Fundamentals · Unit 2: Engineering quantities

Purpose and measurable learning outcomes

Use the SI base quantities and write compound dimensions before evaluating equations. Conversions require complete cancellation of units rather than memorized decimal factors. A mass flow of 720 kg/h is 0.2 kg/s; a pressure of 2 bar is 200 kPa. Distinguish absolute temperature from temperature difference: a 10°C increment equals 10 K, but absolute temperatures are not numerically equal.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

Write numerical units on every stream table entry. Suppose a feed is quoted as 1500 kg/day while the transfer pump is rated in kg/h. A common error is to compare these without dividing by 24, leading to a mistaken 24-fold oversizing. Similar hazards occur between Pa and bar, litres and cubic metres, and mol and kmol. Temperature scaling has a separate pitfall: a 20°C increase is a 20 K difference, but using 20 instead of 293.15 in an absolute thermodynamic expression is incorrect. Check cancellation of dimensions before selecting a calculator.

Governing quantitative relationship

Dimension of dynamic viscosity is M L^-1 T^-1, consistent with Pa·s; 1 Pa·s = 1 kg/(m·s).

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

Convert a volumetric flow of 18 m³/h to litres per second, then convert to mass flow for density 980 kg/m³.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Using degrees Celsius in an ideal-gas formula that requires thermodynamic kelvin.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. Convert a volumetric flow of 18 m³/h to litres per second, then convert to mass flow for density 980 kg/m³. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Using degrees Celsius in an ideal-gas formula that requires thermodynamic kelvin. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 03](../labs/lab-03.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-02.html) · [Book contents](../index.html)

Unit 2.2: Flow rates and concentration measures

Chemical Engineering Fundamentals · Unit 2: Engineering quantities

Purpose and measurable learning outcomes

A stream can be specified by total mass rate, total molar rate, component rate or concentration. Mass fractions sum to one, and mole fractions sum to one, but their numerical values differ when species molar masses differ. State wet versus dry gas basis and percent by mass versus percent by volume. In a reacting stream, compare inlet and outlet component rates on a common molar basis.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

When switching from molar to mass fractions, the molar masses matter. A gas mixture with 50 mol% of a heavy species is not necessarily half that species by mass; its mass fraction is y_i M_i divided by the mixture-average molar mass. Conversely, a liquid with 10 wt% solute cannot be converted to mole fraction until molar masses are provided. A correct mixing problem therefore records every stream’s chosen rate basis and composition convention. Audit whether reported concentrations are by volume, by mass, on dry gas, or in parts per million under specified reference conditions.

Governing quantitative relationship

For a 100 kg/h feed containing 12 wt% solute, solute rate is 12 kg/h and solvent rate 88 kg/h.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

Two liquid solutions of equal density have different solute mass fractions. Determine final fraction from solute mass, not by averaging reported percentages.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Averaging two concentrations without accounting for unequal flowrates.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. Two liquid solutions of equal density have different solute mass fractions. Determine final fraction from solute mass, not by averaging reported percentages. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Averaging two concentrations without accounting for unequal flowrates. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 04](../labs/lab-04.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-02.html) · [Book contents](../index.html)

Unit 2.3: Properties and reference conditions

Chemical Engineering Fundamentals · Unit 2: Engineering quantities

Purpose and measurable learning outcomes

Density, viscosity, vapor pressure and heat capacity can depend strongly on temperature and composition. Specify pressure and reference state when interpreting a property table; never assume a quoted nominal value applies throughout a plant. A measured specific gravity is dimensionless only with a clear reference fluid and temperature. Property models should record the applicability range and uncertainty.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

Most property tables are interpolations of measured data, not nature's eternal constants. Density can change enough with temperature to affect both tank inventory and flowmeter calibration. Viscosity can change pressure drop far more strongly in some fluids. A good sensitivity test obtains lower and upper plausible property values, computes the relevant engineering output at both, and checks whether the design decision changes. If it does, invest in a more appropriate property package or direct measurements. Never infer an accurate viscosity from a single nominal density value.

Governing quantitative relationship

Mass flow = density × volume flow; at 0.85 kg/L and 12 L/min the mass rate is 10.2 kg/min.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A flowmeter is calibrated using water but measures a warm organic liquid. Identify the property information needed before interpreting its indication.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Substituting a room-temperature property in a boiling or high-pressure calculation without testing sensitivity.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A flowmeter is calibrated using water but measures a warm organic liquid. Identify the property information needed before interpreting its indication. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Substituting a room-temperature property in a boiling or high-pressure calculation without testing sensitivity. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 03](../labs/lab-03.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-02.html) · [Book contents](../index.html)

Unit 2.4: Estimation, uncertainty and scale

Chemical Engineering Fundamentals · Unit 2: Engineering quantities

Purpose and measurable learning outcomes

Engineering estimation narrows possible answers before complex computation. Compare orders of magnitude using conservation, bounds and limiting cases. Measurement uncertainty is not fixed by adding digits. When data have correlated biases, root-sum-square propagation under independence is not sufficient. Define an acceptance test in advance: balance closure, plausible density, attainable temperature or equipment capacity.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

An estimate should survive a limiting-case test. In an ideal mixer the outlet concentration must lie between the inlet concentrations when no reaction or separation occurs; a value outside that interval is prima facie evidence of an accounting problem. For a nonreactive splitter, product and waste cannot have a sum of component masses greater than feed. A calculated negative absolute pressure or temperature is physically invalid for ordinary process conditions. These quick tests can flag bad equations before more expensive experimental testing or numerical refinement.

Governing quantitative relationship

For independent uncertainties u1 and u2, combined standard uncertainty u = sqrt(u1²+u2²); 3 and 4 units combine to 5.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

An instrument reports 0.008736 m³/s while the pump nameplate supports roughly 0.001–0.003 m³/s. Propose a data-reconciliation sequence.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Treating a tidy spreadsheet result as proof that field observations were correctly calibrated.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. An instrument reports 0.008736 m³/s while the pump nameplate supports roughly 0.001–0.003 m³/s. Propose a data-reconciliation sequence. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Treating a tidy spreadsheet result as proof that field observations were correctly calibrated. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 04](../labs/lab-04.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-02.html) · [Book contents](../index.html)

Unit 2 applied engineering project — A metering and mixing skid

Setting and purpose

A student pilot line measures liquid feed rates by two meters of different calibration history. One stream is in L/min and the other in kg/h. This is a synthetic teaching case, not a recommendation to operate a real process. Students must select reasonable illustrative numbers, label every invented number as an assumption, and keep all units, reference conditions and composition bases visible. The purpose is to assemble the unit's concepts into a consistent model that a reviewer can challenge.

Engineering question

Create a dimensional audit, identify uncertainty and evaluate how a density error would affect a target blend composition. State a single primary decision being supported, such as selecting a material-balance boundary, accepting a measurement, identifying a missing outlet or prioritizing an additional experiment. Do not use an unsupported plant-wide profit number or an unverified regulatory threshold to justify the decision.

Required evidence and calculation plan

1. Write a process statement that defines input materials, expected outputs and the relevant boundaries. Distinguish a batch inventory from a flow and give the measurement time basis.
2. Build an input data table with dimensions, source type, uncertainty estimate and acceptable bounds. Separate readings from engineering assumptions.
3. Derive at least three equations rather than relying only on a calculator. For each, show a dimensional check and a feasible limiting case. Include a separate component balance when a concentration or reaction is involved.
4. Carry out two contrasting cases: a nominal baseline and a plausible changed operating condition. If the changed condition violates the simplified model, stop and write that result as an important finding.
5. Use the unit laboratories as computational demonstrations; export plots, retain input settings, and compare with a direct hand calculation. Plots are evidence about a mathematical model, not proof about an operating plant.
6. Describe data or safety limitations. Include possible missing streams, property correlations, instrument bias, parameter dependence and common-cause uncertainty where they matter.
7. Communicate the result as a reproducible engineering note with an executive statement, flow diagram, equations, tables, a source list and an open list of unresolved questions.

Review checkpoints

• Conservation: material and energy accounting closure must be explicit; an unresolved residual is named, not silently forced to zero.
• Feasibility: compositions must be physically bounded and equipment temperatures and pressures checked against the model's assumptions.
• Traceability: a competent reader can identify exactly which values are assumed, measured or derived, and can reproduce the major quantities.
• Safety and ethics: no classroom calculation is presented as industrial relief sizing, pharmaceutical validation, field authorization or environmental compliance proof.

Deliverables

Submit one concise process diagram, one independently checkable calculation sheet, two simulation exports, a one-page uncertainty/sensitivity commentary and a 250-word statement on what evidence would change your conclusion. Defend the chosen model scope and openly identify a more advanced analysis needed before industrial deployment.

Unit 2 assessment: Engineering quantities

These 12 problems combine quantitative reproduction, model validity, and audit methodology. Answers below are intended as diagnostic reasoning, not fabricated plant data.

Question 1: analysis of si units and dimensional consistency

Convert a volumetric flow of 18 m³/h to litres per second, then convert to mass flow for density 980 kg/m³.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 2.1. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 2: model validity

Using degrees Celsius in an ideal-gas formula that requires thermodynamic kelvin. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 3: quantitative audit

Use the lesson's worked equation: Dimension of dynamic viscosity is M L^-1 T^-1, consistent with Pa·s; 1 Pa·s = 1 kg/(m·s). Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 5: analysis of flow rates and concentration measures

Two liquid solutions of equal density have different solute mass fractions. Determine final fraction from solute mass, not by averaging reported percentages.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 2.2. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 6: model validity

Averaging two concentrations without accounting for unequal flowrates. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 7: quantitative audit

Use the lesson's worked equation: For a 100 kg/h feed containing 12 wt% solute, solute rate is 12 kg/h and solvent rate 88 kg/h. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 9: analysis of properties and reference conditions

A flowmeter is calibrated using water but measures a warm organic liquid. Identify the property information needed before interpreting its indication.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 2.3. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 10: model validity

Substituting a room-temperature property in a boiling or high-pressure calculation without testing sensitivity. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 11: quantitative audit

Use the lesson's worked equation: Mass flow = density × volume flow; at 0.85 kg/L and 12 L/min the mass rate is 10.2 kg/min. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 13: analysis of estimation, uncertainty and scale

An instrument reports 0.008736 m³/s while the pump nameplate supports roughly 0.001–0.003 m³/s. Propose a data-reconciliation sequence.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 2.4. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 14: model validity

Treating a tidy spreadsheet result as proof that field observations were correctly calibrated. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 15: quantitative audit

Use the lesson's worked equation: For independent uncertainties u1 and u2, combined standard uncertainty u = sqrt(u1²+u2²); 3 and 4 units combine to 5. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.