Chapter 4 - Control Volume Analysis Using Energy

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Questions and Answers

What happens to the velocity of a gas or liquid in a diffuser?

It increases in the direction of flow.

It remains constant throughout the passage.

It fluctuates randomly.

It decreases in the direction of flow. (correct)

Which energy changes can be neglected in turbine modeling if they are minimal?

Change in potential energy. (correct)

Change in internal energy.

Change in enthalpy.

Change in kinetic energy. (correct)

What distinguishes a compressor from a pump?

A compressor is always larger than a pump.

A compressor can only operate at low pressures.

A compressor operates only with gases, while a pump operates with liquids. (correct)

A pump increases the temperature of the liquid.

In which heat exchanger type do hot and cold streams mix directly?

Direct contact. Signup and view all the answers

What must be ensured regarding units when performing calculations involving turbines, compressors, or heat exchangers?

Units must be consistent, converting between kW and W when necessary. Signup and view all the answers

Which condition is typically neglected in pump or compressor modeling when considering energy changes?

Change in kinetic energy. Signup and view all the answers

In a tube-within-a-tube counterflow heat exchanger, how do the streams flow?

In opposite directions. Signup and view all the answers

What must be considered when neglecting energy changes in flow systems?

Both kinetic and potential energy changes can be neglected at the same time. Signup and view all the answers

What characterizes a steady-state control volume?

All properties remain constant over time. Signup and view all the answers

Which equation represents the mass rate balance for a control volume with multiple inlets and exits?

$\frac{dm_{cv}}{dt} = \sum \dot{m}{in} - \sum \dot{m}{out}$ Signup and view all the answers

What does one-dimensional flow imply in a mass flow rate scenario?

Flow is perpendicular to the boundary at entry and exit points. Signup and view all the answers

Which of the following best differentiates mass flow rate from volumetric flow rate?

Mass flow rate is measured in kg/s; volumetric flow rate is in m³/s. Signup and view all the answers

In the context of control volume analysis, what is the implication of having multiple inlets?

The mass flow rates at each inlet are additive. Signup and view all the answers

Which component is typically analyzed using control volume methods?

A heat exchanger Signup and view all the answers

What does it mean if there is a time rate of change of mass contained within a control volume?

The flow is unsteady. Signup and view all the answers

Which of the following is NOT a component typically analyzed in engineering using control volume models?

Friction brake Signup and view all the answers

What does the mass rate balance for a control volume account for in steady-state conditions?

Unchanging properties of the system over time Signup and view all the answers

Which equation is used to express work in the context of energy transfer in a control volume?

Eq. 4.12 Signup and view all the answers

What is the role of enthalpy in the control volume energy rate balance?

It simplifies the calculation of energy transfer through variations in pressure and volume. Signup and view all the answers

In the context of a nozzle, what happens to the velocity of a gas or liquid as it passes through?

It increases due to the varying cross-sectional area. Signup and view all the answers

Which of the following equations represents the net rate of energy transfer into the control volume?

Eq. 4.15 Signup and view all the answers

What condition must be met for the first law of thermodynamics to apply to open systems at steady-state?

All system properties must remain constant over time. Signup and view all the answers

What does Eq. 4.20a represent in the context of control volumes?

The energy conservation principle in a one-inlet, one-exit system. Signup and view all the answers

What type of control volume application may involve the use of throttling devices?

Systems where pressures are significantly reduced. Signup and view all the answers

What is a throttling device primarily used for?

To significantly reduce pressure in a fluid line Signup and view all the answers

Which of the following conditions must be true for the term involving potential energy to drop out of the energy balance equation?

Change in potential energy is negligible Signup and view all the answers

What does the term 'transient' refer to in the context of mass balance?

State change occurring with time Signup and view all the answers

When applying the first law of thermodynamics to open systems, which analysis is primarily considered?

Transient analysis Signup and view all the answers

What is intended by system integration in engineering?

Combining components to achieve objectives under constraints Signup and view all the answers

For the energy balance to ignore kinetic and potential energy effects, what condition must hold true?

Specific enthalpies at inlets and exits are constant with time Signup and view all the answers

What must be integrated to perform transient analysis of mass balance?

Mass rate balance from time 0 to t Signup and view all the answers

In the context of throttling devices, which method is commonly used to introduce a restriction in fluid flow?

Partially opened valve or porous plug Signup and view all the answers

Study Notes

Control Volume Analysis Using Energy

Learning Outcomes (General): Distinguish between steady-state and transient control volume analyses. Differentiate between mass flow rate and volumetric flow rate. Explain one-dimensional flow and flow work. Apply mass and energy balances to control volumes, developing engineering models for practical components. Obtain and apply appropriate property data for control volume analyses.

Mass Rate Balance

Basic Equation (1 of 4): The time rate of change of mass within a control volume (dm_cv/dt) equals the difference between the mass flow rate in (ṁ_i) and the mass flow rate out (ṁ_e) .
Multiple Inlets/Exits (3 of 4): The general equation for control volumes with multiple inlets/exits is ṁ_cv = ∑ṁ_i - ∑ṁ_e
One-Dimensional Flow (7): Flow is perpendicular to the boundary at locations where mass enters or leaves the control volume. Intensive properties are uniform across each inlet or exit area.
Steady-State (8): In steady-state analysis, all properties are constant with time; therefore, dṁ_cv/dt = 0. The mass flow rate in equals the mass flow rate out ( ∑ṁ_i = ∑ṁ_e).

Energy Rate Balance

Governing Equation (9): The time rate of change of energy within a control volume (dE_cv/dt) is equal to the net rate at which energy is transferred in by heat transfer ( ṁ_i (h_i + V_i²/2 + g z_i) - ṁ_e (h_e + V_e²/2 + g z_e) ). This also includes the rate of work done.
Work (10): The expression for work includes contributions from rotating shafts, boundary displacement, and electrical effects. Flow work is also at inlets and outlets.
One-Dimensional Flow Form (11,12): The energy balance equation considers enthalpy ( h_i,e), velocity ( V²_i,e), gravitational elevation changes ( gz_i,e), and heat input in different sections of the control volume. Summation over the inlets and exits is necessary.
Steady State (13): In steady state, dU_cv/dt = 0; ∑ṁ_i(h_i + V_i²/2 + g z_i ) = ∑ṁ_e(h_e + V_e²/2 + g z_e).

Specific Component Modeling

Nozzles and Diffusers (16, 17): Nozzle: flow area decreases causing velocity increase, Diffuser: flow area increases causing velocity to decrease.
Turbines (19, 20): A device which uses flowing fluid (gas or liquid) passing through blades attached to a rotating shaft and converts fluid energy into work.
Compressors and Pumps (21, 22): Devices that use work to change the state of a fluid (gas or liquid), typically to elevate pressure.
Heat Exchangers (23, 24): Components for transferring heat between two fluids. Direct contact involves mixing fluids. Tube-within-a-tube, uses a wall for conduction between fluids.

Throttling Devices (25,26)

Throttling Device: A device that causes a significant decrease in pressure by introducing a restriction to the flow of a gas or liquid. The process is considered isenthalpic, meaning enthalpy remains constant (h₂ = h₁).

System Integration (27)

System Integration: Engineers creatively combine components to achieve a desired overall objective, within specified constraints (like cost).

Transient Analysis

Mass Balance (29, 30): The change in mass within the control volume, integrated from initial to final time equals, net mass flow rate in minus net mass flow rate out.
Energy Balance (31): The change in internal energy within the control volume, summed over time, is equivalent to net heat transfer (Q_cv ), net work (W_cv), and change in enthalpy summed across inlets and outlets.

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Description

This quiz covers key concepts in fluid dynamics, including the behavior of gases and liquids in various systems such as diffusers, turbines, compressors, and heat exchangers. It explores energy changes, flow characteristics, and important distinctions between flow types. Ideal for students of engineering or fluid mechanics.