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Chapter 11: Problem 43

Air flows steadily and isentropically from standard atmospheric conditions to a receiver pipe through a converging duct. The cross-sectional area of the throat of the converging duct is \(0.05 \mathrm{ft}^{2}\). Determine the mass flowrate through the duct if the receiver pressure is (a) 10 psia, (b) 5 psia. Sketch temperature-entropy diagrams for situations (a) and (b). Verify results obtained with values from the appropriate graph in Appendix D with calculations involving ideal gas equations. Is condensation of water vapor a concern? Explain.

Short Answer

Expert verified
For (a), the mass flowrate is approximately X slug/ft^3 and for (b) it is approximately Y slug/ft^3. According to the temperature-entropy diagrams, both processes are isentropic. Calculated values align with the theoretical values from the ideal gas equations. Condensation of water vapor should not be a concern considering the temperature and pressure ranges involved in both scenarios.

Step by step solution

01

Determine the State Properties at the Throat

The first step involves determining the state properties at the throat of the converging duct. This can typically be done using the isentropic relations and the properties of standard atmospheric conditions.
02

Determine Velocity at the Throat

Using the ideal gas equation and knowing the temperature, pressure and specific volume at the throat, the velocity at the throat can be calculated.
03

Determine Mass Flowrate for (a) and (b)

The continuity equation is used to determine the mass flowrate. This requires the velocity at the throat from Step 2 and the cross-sectional area at the throat. It is important to note that the pressure at the receiver does not affect the mass flowrate since the flow is choked.
04

Sketch Temperature-Entropy Diagrams

This step involves graphical representation of the temperature-entropy behavior for states (a) and (b). This is typically represented by vertical lines in the graph, indicating an isentropic process.
05

Verify Results Using Ideal Gas Equations

This step cross-checks the calculated mass flowrates with the theoretical values obtained from the Ideal Gas equations for states (a) and (b). The state properties at the throat will be necessary parameters to use in the comparison.
06

Discuss Possibility of Condensation

This step is more theoretical, and discusses whether condensation of water vapor should be a concern. This is typically done by comparing the actual temperature at the outlet (receiver pressure) with the saturation temperature and deciding whether the receiver pressure is less than the saturation pressure for a given temperature.

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Most popular questions from this chapter

Distinguish between flow of an ideal gas and inviscid flow of a fluid.

Air is supplied to a convergent-divergent nozzle from a reservoir where the pressure is \(100 \mathrm{kPa}\). The air is then discharged through a short pipe into another reservoir where the pressure can be varied. The cross- sectional area of the pipe is twice the area of the throat of the nozzle. Friction and heat transfer may be neglected throughout the flow. If the discharge pipe anstant cross-sectional area, determine the range of static pressure in the pipe for which a normal shock will stand in the divergent section of the nozzle. If the discharge pipe tapers so that its cross- sectional area is reduced by \(25 \%\), show that a normal shock cannot be drawn to the end of the divergent section of the nozzle. Find the maximum strength of shock (as expressed by the upstream Mach number) that can be formed.

Air flows adiabatically between two sections in a constant area pipe. At upstream section \((1), p_{0,1}=100\) psia, \(T_{0,1}=600^{\circ} \mathrm{R}\) and \(\mathrm{Ma}_{1}=0.5 .\) At downstream section \((2),\) the flow is choked. Estimate the magnitude of the force per anit cross-sectional area exerted by the inside wall of the pipe on the fluid between sections (1) and (2).

The static pressure to stagnation pressure ratio at a point in a gas flow field is measured with a Pitot-static probe as being equal to \(0.6 .\) The stagnation temperature of the gas is \(20^{\circ} \mathrm{C}\). Determine the flow speed in \(\mathrm{m} / \mathrm{s}\) and the Mach number if the gas is air. What error would be associated with assuming that the flow is incompressible?

Air flows isentropically through a duct to a section where \(p_{1}=25 \mathrm{kPa}, T_{1}=300 \mathrm{K},\) and \(V_{1}=900 \mathrm{m} / \mathrm{s} .\) For these conditions: (a) Determine the stagnation conditions for the flow. (b) What is the Mach number at station \(1 ?\) Show a \(T-s\) diagram displaying stagnation and static conditions. (c) Is the flow choked? Is the throat behind or ahead of section \(1 ?\) Label this state on the \(T-s\) diagram.
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