Chapter 4: Control volume analysis using energy

MC Questions for exam 2

A flow idealized as a throttling process through a device has: h₂ > h₁ and p₂ < p₁ h₂ > h₁ and p₂ > p₁ h₂ = h₁ and p₂ > p₁ h₂ = h₁ and p₂ < p₁ ans. D Explanation: Although counter intuitive, velocity is increased at the end of a throttle, but pressure is reduced. Think of a garden hose, which is an example of a nozzle: the water flows at a higher spreed out of the nozzle, and we know that the hose water is providing pressure, but the high pressure point is actually the area right before entering the nozzle. The tight shape allows a pressure drop that increase exit velocity. Same concept here. Steady flow devices that result in a drop in working fluid pressure from inlet to exit are: Nozzle, pump, throttling device. Diffuser, pump, throttling device. Diffuser, turbine, throttling device. Nozzle, turbine, throttling device. ans. D At steady state, conservation of energy asserts the total rate at which energy is transferred into the control volume equals the total rate at which energy is transferred out. True False ans. True For a control volume at steady state, mass can accumulate within the control volume. True False ans. False Factors that may allow one to model a control volume as having negligible (zero) heat transfer include (1) the outer surface of the control volume is well insulated, (2) the outer surface area of the control volume is too small to permit effective heat transfer, (3) the temperature difference between the control volume and its surroundings is so small that the heat transfer can be ignored, and (4) the working fluid passes through the control volume so quickly that there is not enough time for significant heat transfer to occur. True False ans. True Flow work is the work done on a flowing stream by a paddle wheel or piston. True False ans. False

Nozzles and Diffusers

A nozzle is a flow passage of varying cross-sectional area in which the velocity of a gas or liquid increases in the direction of flow. In a diffuser, the gas or liquid decelerates in the direction of flow. Steady-State form of energy rate balance: 0 = m[(h₁-h₂)+(v₁²-v₂²/2)] 1. One-inlet, one exit control volume at steady-state. 2. ∆PE is negligible 3. There is no significant heat transfer between the nozzle and its surroundings. 4. No work is associated with the nozzle.

Throttling devices

A throttling device is a device that achieves A significant reduction in pressure can be achieved simply by introducing a restriction into a line through which a gas or liquid flows. This is commonly done by means of a partially opened valve or a porous plug. Steady-State form of energy rate balance: h₁ = h₂ 1. ∆PE is negligible. There is usually no significant heat transfer with the surroundings, and the change in potential energy from inlet to exit is negligible. 2. There is no significant heat transfer between the throttling device and its surroundings. 3. No work is associated with the throttling device.the only work is flow work at locations where mass enters and exits the control volume, so the term W_cv drops out of the energy rate balance. 4. Although velocities may be relatively high in the vicinity of the restriction imposed by the throttling device on the flow through it, measurements made upstream and downstream of the reduced flow area is such that change in kinetic energy between these locations can be neglected.

Turbines

A turbine is a device in which power is developed as a result of a gas or liquid passing through a set of blades attached to a shaft free to rotate. Such turbines are widely used for power generation in vapor power plants, gas turbine power plants, and aircraft engines (see Chaps. 8 and 9). In these applications, super heated steam or a gas enters the turbine and expands to a lower pressure as power is generated. Steady-State form of energy rate balance: 0 = -W_cv + m(h₁-h₂) 1. ∆PE & ∆KE is negligible 2. There is no significant heat transfer between the turbine and its surroundings.

Heat Exchangers

As shown by Fig. 4.13, heat exchangers can involve multiple inlets and exits. Heat exchangers have innumerable domestic and industrial applications, including use in home heating and cooling systems, automotive systems, electrical power generation, and chemical processing. Steady-State form of energy rate balance: 0 = m₁h₁ +m₃h₃ - m₂h₂ - m₄h₄ 1. ∆PE & ∆KE is negligible. In addition, the kinetic and potential energies of the flowing streams usually can be ignored at the inlets and exits. 2. There is no significant heat transfer between the heat exchanger and its surroundings. Although high rates of energy transfer within the heat exchanger occur, heat transfer with the surroundings is often small enough to be neglected. 3. No work is associated with the heat exchanger. For a control volume enclosing a heat exchanger, the only work is flow work at the places where matter enters and exits, so the term W˙cv drops out of the energy rate balance

Compressors and pumps

Compressors and pumps are devices in which work is done on the substance flowing through them in order to change the state of the substance, typically to increase the pressure and/or elevation. The term compressor is used when the substance is a gas (vapor) and the term pump is used when the substance is a liquid. Steady-State form of energy rate balance: 0 = -W_cv + m(h₁-h₂) 1. ∆PE & ∆KE is negligible 2. There is no significant heat transfer between the turbine and its surroundings. For liquids liquid is incomprehensible (v is constant).

1-D flow form of control volume energy rate balance

dE_cv/dt = Q_cv - W_cv + ∑m_i(h_i + v_i²/2 + g*z_i) - ∑m_e(h_e + v_e²/2 + g*z_e) The LHS is the time rate of change of energy contained within the control volume at time t. The RHS is: - The net rate at which energy is being transferred in by heat transfer a time t (1st term). - The net rate at which energy is being transferred out by work at time t - namely by flow work at exit e and inlet i and by other forms of work (2nd term) - the net rate energy is transferred in at inlet, i and exit e accompanying mass flow (3rd & 4th terms) For a control volume at steady state, the conditions of the mass within the control volume and at the boundary do not vary with time. The mass flow rates and the rates of energy transfer by heat and work are also const. with time. At steady state dE_cv/dt = 0.