Question 1

Which of the following best describes the continuity equation for a steady-state open system with a single inlet and outlet?

Accepted Answer

$$\Delta (\rho v A)_{fs} = 0$$

Question 2

A liquid flows through a pipe with a diameter of 4 cm at a volumetric flow rate of $$0.002 \ m^3$/s. $$What is the average velocity of the liquid in the pipe?

Accepted Answer

$$v = \frac{q}{A} = \frac{0.002}{\frac{\pi}{4}(0.04)^2$} = 1.59 \ m/s$$

Question 3

In the context of open systems, which of the following is NOT a correct expression for mass flow rate?

Accepted Answer

$$\dot{m} = v q$$

Question 4

A major human artery with an internal diameter of 5 mm carries blood at a volumetric flow rate of $$5 \ cm^3$/s. $$After bifurcating into two arteries of 3 mm diameter each, what is the velocity of blood in each branch?

Accepted Answer

$$v = \frac{2.5 \ cm^3$/s}{\frac{\pi}{4}(0.3 \ cm)^2$} = 35.4 \ cm/s$$

Question 5

For a steady-state open system, which statement is TRUE?

Accepted Answer

The inflow of mass equals the outflow of mass.

Question 6

Liquid n-hexane flows at $$0.75 \ kg/s in a $$pipe of diameter $$5 \ cm. If $$the density is $$659 \ kg/m^3$, what is the volumetric flow rate q$?

Accepted Answer

$$q = \frac{0.75}{659} = 0.00114 \ m^3$/s$$

Question 7

Which of the following best represents the energy carried by a unit mass of fluid in a flowing stream?

Accepted Answer

$$U + \frac{v^2$}{2} + zg$$

Question 8

If the cross-sectional area of a pipe is halved while keeping the volumetric flow rate constant, what happens to the average velocity of the fluid?

Accepted Answer

It quadruples.

Question 9

In the energy balance for an open system, which term is omitted in the absence of flowing streams (i.e., for a closed system)?

Accepted Answer

$$\sum_{in} \dot{m}(U + \frac{v^2$}{2} + gz)$$

Question 10

A control volume is best described as:

Accepted Answer

A fixed region in space through which mass and energy can flow.

Question 11

Which of the following is the correct formula for the molar flow rate $$\dot{n} in $$terms of mass flow rate $$\dot{m}$$ and molar mass $$M$$?

Accepted Answer

$$\dot{n} = \frac{\dot{m}}{M}$$

Question 12

In a steady-state process, which of the following is always true?

Accepted Answer

The mass inside the control volume is constant.

Question 13

Which of the following is NOT a form of work associated with open systems?

Accepted Answer

Work associated with chemical reaction enthalpy

Question 14

If the density of a fluid doubles while keeping the mass flow rate and pipe diameter constant, what happens to the average velocity?

Accepted Answer

It is halved.

Question 15

Which of the following equations correctly reduces to $$\Delta U_t = Q + W$$ for a closed system?

Accepted Answer

$$\frac{d(mU)_{cv}}{dt} = Q + W$$

Question 16

A process is at steady state if:

Accepted Answer

The mass and energy within the control volume do not change with time.

Question 17

Which of the following is a correct statement about the mass balance for a control volume?

Accepted Answer

$$\frac{dm_{cv}}{dt} + \Delta (\dot{m})_{fs} = 0$$

Question 18

A pipe carries water at a mass flow rate of $$2 \ kg/s$$ and a density of $$1000 \ kg/m^3$. What is the volumetric flow rate?

Accepted Answer

$$q = \frac{2}{1000} = 0.002 \ m^3$/s$$

Question 19

Which of the following is a correct interpretation of the term $$\Delta (\rho v A)_{fs} in $$the mass balance equation?

Accepted Answer

It represents the net mass flow rate into and out of the control volume.

Energy and Mass Balances for Open Systems in Chemical Engineering Thermodynamics

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