Chapter 4

Air enters a water-jacketed air compressor operating at steady state with a volumetric flow rate of $37{\mathrm{m}}^3/\min$ at 136 $\mathrm{kPa},305\mathrm{K}$ and exits with a pressure of $680\mathrm{kPa}$ and a temperature of $400\mathrm{K}$. The power input to the compressor is $155\mathrm{kW}$. Energy transfer by heat from the compressed air to the cooling water circulating in the water jacket results in an increase in the temperature of the cooling water from inlet to exit with no change in pressure. Heat transfer from the outside of the jacket as well as all kinetic and potential energy effects can be neglected. (a) Determine the temperature increase of the cooling water, in $\mathrm{K}$, if the cooling water mass flow rate is $82\mathrm{kg}/\min$. (b) Plot the temperature increase of the cooling water, in $\mathrm{K}$, versus the cooling water mass flow rate ranging from 75 to $90\mathrm{kg}/\min$.

A pump steadily delivers water through a hose terminated by a nozzle. The exit of the nozzle has a diameter of $2.5\mathrm{cm}$ and is located $4\mathrm{m}$ above the pump inlet pipe, which has a diameter of $5.0\mathrm{cm}$. The pressure is equal to 1 bar at both the inlet and the exit, and the temperature is constant at ${20}^{\circ }\mathrm{C}$. The magnitude of the power input required by the pump is $8.6\mathrm{kW}$, and the acceleration of gravity is $g=9.81\mathrm{m}/{\mathrm{s}}^2$. Determine the mass flow rate delivered by the pump, in $\mathrm{kg}/\mathrm{s}$.

An oil pump operating at steady state delivers oil at a rate of $5.5\mathrm{kg}/\mathrm{s}$ and a velocity of $6.8\mathrm{m}/\mathrm{s}$. The oil, which can be modeled as incompressible, has a density of $1600\mathrm{kg}/{\mathrm{m}}^3$ and experiences a pressure rise from inlet to exit of $28\mathrm{Mpa}$. There is no significant elevation difference between inlet and exit, and the inlet kinetic energy is negligible. Heat transfer between the pump and its surroundings is negligible, and there is no significant change in temperature as the oil passes through the pump. If pumps are available in $1/4$-horsepower increments, determine the horsepower rating of the pump needed for this application.

Ammonia enters a heat exchanger operating at steady state as a superheated vapor at 14 bar, ${60}^{\circ }\mathrm{C}$, where it is cooled and condensed to saturated liquid at 14 bar. The mass flow rate of the refrigerant is $450\mathrm{kg}/\mathrm{h}$. A separate stream of air enters the heat exchanger at ${17}^{\circ }\mathrm{C},1$ bar and exits at ${42}^{\circ }\mathrm{C},1$ bar. Ignoring heat transfer from the outside of the heat exchanger and neglecting kinetic and potential energy effects, determine the mass flow rate of the air, in $\mathrm{kg}/\min$.

Carbon dioxide gas is heated as it flows steadily through a 2.5-cm-diameter pipe. At the inlet, the pressure is 2 bar, the temperature is $300\mathrm{K}$, and the velocity is $100\mathrm{m}/\mathrm{s}$. At the exit, the pressure and velocity are $0.9413$ bar and $400\mathrm{m}/\mathrm{s}$, respectively. The gas can be treated as an ideal gas with constant specific heat $c_p=0.94\mathrm{kJ}/\mathrm{kg}\cdot \mathrm{K}$. Neglecting potential energy effects, determine the rate of heat transfer to the carbon dioxide, in $\mathrm{kW}$.

Figure P4.44 shows a solar collector panel with a surface area of $2.97{\mathrm{m}}^2$. The panel receives energy from the sun at a rate of $1.5\mathrm{kW}$. Thirty-six percent of the incoming energy is lost to the surroundings. The remainder is used to heat liquid water from ${40}^{\circ }\mathrm{C}$ to ${60}^{\circ }\mathrm{C}$. The water passes through the solar collector with a negligible pressure drop. Neglecting kinetic and potential energy effects, determine at steady state the mass flow rate of water, in $\mathrm{kg}.$ How many gallons of water at ${60}^{\circ }\mathrm{C}$ can eight collectors provide in a 30 -min time period?

A feedwater heater operates at steady state with liquid water entering at inlet 1 at 7 bar, ${42}^{\circ }\mathrm{C}$, and a mass flow rate of $70\mathrm{kg}/\mathrm{s}$. A separate stream of water enters at inlet 2 as a two-phase liquid-vapor mixture at 7 bar with a quality of $98\mathrm{\%}$. Saturated liquid at 7 bar exits the feedwater heater at 3 . Ignoring heat transfer with the surroundings and neglecting kinetic and potential energy effects, determine the mass flow rate, in $\mathrm{kg}/\mathrm{s}$, at inlet 2 .

The electronic components of a computer consume $0.1\mathrm{kW}$, of electrical power. To prevent overheating, cooling air is supplied by a 25-W fan mounted at the inlet of the electronics enclosure. At steady state, air enters the fan at ${20}^{\circ }\mathrm{C},1$ bar and exits the electronics enclosure at ${35}^{\circ }\mathrm{C}$. There is no significant energy transfer by heat from the outer surface of the enclosure to the surroundings and the effects of kinetic and potential energy can be ignored. Determine the volumetric flow rate of the entering air, in ${\mathrm{m}}^3/\mathrm{s}$.

Ten $\mathrm{kg}/\min$ of cooling water circulates through a water jacket enclosing a housing filled with electronic components. At steady state, water enters the water jacket at ${22}^{\circ }\mathrm{C}$ and exits with a negligible change in pressure at a temperature that cannot exceed ${26}^{\circ }\mathrm{C}$. There is no significant energy transfer by heat from the outer surface of the water jacket to the surroundings, and kinetic and potential energy effects can be ignored. Determine the maximum electric power the electronic components can receive, in $\mathrm{kW}$, for which the limit on the temperature of the exiting water is met.

Propane vapor enters a valve at $1.6\mathrm{MPa},{70}^{\circ }\mathrm{C}$, and leaves at $0.5\mathrm{MPa}$. If the propane undergoes a throttling process, what is the temperature of the propane leaving the valve, in ${}^{\circ }\mathrm{C}$ ?