Chapter 5: Problem 65
A well-insulated valve is used to throttle steam from \(8 \mathrm{MPa}\) and \(350^{\circ} \mathrm{C}\) to \(2 \mathrm{MPa}\). Determine the final temperature of the steam.
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Consider a 35 -L evacuated rigid bottle that is surrounded by the atmosphere at \(100 \mathrm{kPa}\) and \(22^{\circ} \mathrm{C}\). A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle during this filling process.
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 \(r\).
In large gas-turbine power plants, air is preheated by the exhaust gases in a heat exchanger called the regenerator before it enters the combustion chamber. Air enters the regenerator at \(1 \mathrm{MPa}\) and \(550 \mathrm{K}\) at a mass flow rate of \(800 \mathrm{kg} / \mathrm{min}\). Heat is transferred to the air at a rate of \(3200 \mathrm{kJ} / \mathrm{s}\). Exhaust gases enter the regenerator at \(140 \mathrm{kPa}\) and \(800 \mathrm{K}\) and leave at \(130 \mathrm{kPa}\) and \(600 \mathrm{K}\). Treating the exhaust gases as air, determine ( \(a\) ) the exit temperature of the air and \((b)\) the mass flow rate of exhaust gases.
An air-conditioning system requires airflow at the main supply duct at a rate of \(130 \mathrm{m}^{3} / \mathrm{min}\). The average velocity of air in the circular duct is not to exceed \(8 \mathrm{m} / \mathrm{s}\) to avoid excessive vibration and pressure drops. Assuming the fan converts 80 percent of the electrical energy it consumes into kinetic energy of air, determine the size of the electric motor needed to drive the fan and the diameter of the main duct. Take the density of air to be \(1.20 \mathrm{kg} / \mathrm{m}^{3}\).
Hot combustion gases (assumed to have the properties of air at room temperature) enter a gas turbine at \(1 \mathrm{MPa}\) and \(1500 \mathrm{K}\) at a rate of \(0.1 \mathrm{kg} / \mathrm{s}\), and exit at \(0.2 \mathrm{MPa}\) and \(900 \mathrm{K} .\) If heat is lost from the turbine to the surroundings at a rate of \(15 \mathrm{kJ} / \mathrm{s}\), the power output of the gas turbine is \((a) 15 \mathrm{kW}\) (b) \(30 \mathrm{kW}\) \((c) 45 \mathrm{kW}\) \((d) 60 \mathrm{kW}\) \((e) 75 \mathrm{kW}\)
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