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Chapter 5: Problem 23

A diffuser is an adiabatic device that decreases the kinetic energy of the fluid by slowing it down. What happens to this lost kinetic energy?

Short Answer

Expert verified
Answer: The lost kinetic energy is converted into internal energy, specifically potential energy and thermal energy, maintaining the conservation of energy principle.

Step by step solution

01

Introducing a Diffuser

A diffuser is a device that is used to slow down the flow of a fluid, such as air or water, in a controlled manner. This is achieved by increasing the cross-sectional area of the passage through which the fluid flows. In the context of this problem, the diffuser is adiabatic, which means that there is no exchange of heat with the surroundings.
02

Conservation of Energy

In any adiabatic process, the total energy of the system remains constant. This means that if the kinetic energy of the fluid decreases, another form of energy should increase to maintain the conservation of energy.
03

Conversion of Kinetic Energy

As the fluid slows down in the diffuser, its kinetic energy decreases. Considering the conservation of energy, this lost kinetic energy is converted to another form of energy, in this case, internal energy. This internal energy includes potential energy and thermal energy of the fluid particles.
04

Internal Energy Increase

The increase in internal energy, as mentioned, can be due to an increase in potential energy or thermal energy. In a diffuser, the potential energy increases if the fluid is forced to flow in an upward direction against gravity. The thermal energy increase is due to the fluid particles slowing down and, as a result, colliding more frequently with each other, which causes the temperature to rise.
05

Conclusion

In conclusion, the lost kinetic energy in a diffuser is converted into internal energy; specifically, potential energy and thermal energy. In an adiabatic diffuser, this conversion of energy maintains the conservation of energy, as there is no exchange of heat with the surroundings.

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Most popular questions from this chapter

A \(0.3-m^{3}\) rigid tank initially contains refrigerant\(134 \mathrm{a}\) at \(14^{\circ} \mathrm{C}\). At this state, 55 percent of the mass is in the vapor phase, and the rest is in the liquid phase. The tank is connected by a valve to a supply line where refrigerant at \(1.4 \mathrm{MPa}\) and \(100^{\circ} \mathrm{C}\) flows steadily. Now the valve is opened slightly, and the refrigerant is allowed to enter the tank. When the pressure in the tank reaches \(1 \mathrm{MPa}\), the entire refrigerant in the tank exists in the vapor phase only. At this point the valve is closed. Determine ( \(a\) ) the final temperature in the tank, \((b)\) the mass of refrigerant that has entered the tank, and \((c)\) the heat transfer between the system and the surroundings.

The velocity of a liquid flowing in a circular pipe of radius \(R\) varies from zero at the wall to a maximum at the pipe center. The velocity distribution in the pipe can be represented as \(V(r),\) where \(r\) is the radial distance from the pipe center. Based on the definition of mass flow rate \(\dot{m}\) obtain a relation for the average velocity in terms of \(V(r)\) \(R,\) and \(r\).

An ideal gas expands in an adiabatic turbine from \(1200 \mathrm{K}\) and \(900 \mathrm{kPa}\) to \(800 \mathrm{K}\). Determine the turbine inlet volume flow rate of the gas, in \(\mathrm{m}^{3} / \mathrm{s}\), required to produce turbine work output at the rate of \(650 \mathrm{kW}\). The average values of the specific heats for this gas over the temperature range and the gas constant are \(c_{p}=1.13 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, c_{v}=\) \(0.83 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K},\) and \(R=0.30 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\).

The air in a \(6-m \times 5-m \times 4-m\) hospital room is to be completely replaced by conditioned air every 15 min. If the average air velocity in the circular air duct leading to the room is not to exceed \(5 \mathrm{m} / \mathrm{s}\), determine the minimum diameter of the duct.

A balloon that initially contains \(50 \mathrm{m}^{3}\) of steam at \(100 \mathrm{kPa}\) and \(150^{\circ} \mathrm{C}\) is connected by a valve to a large reservoir that supplies steam at \(150 \mathrm{kPa}\) and \(200^{\circ} \mathrm{C}\). Now the valve is opened, and steam is allowed to enter the balloon until the pressure equilibrium with the steam at the supply line is reached. The material of the balloon is such that its volume increases linearly with pressure. Heat transfer also takes place between the balloon and the surroundings, and the mass of the steam in the balloon doubles at the end of the process. Determine the final temperature and the boundary work during this process.
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