Chapter 11: Problem 32
At some point for air flow in a duct, \(p=20\) psia, \(T=500^{\circ} \mathrm{R}\) and \(V=500 \mathrm{ft} / \mathrm{s}\). Can a normal shock occur at this point?
Chapter 11: Problem 32
At some point for air flow in a duct, \(p=20\) psia, \(T=500^{\circ} \mathrm{R}\) and \(V=500 \mathrm{ft} / \mathrm{s}\). Can a normal shock occur at this point?
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Get started for freeShow that for Rayleigh flow, the maximum amount of heat that may be added to the gas is given by: \\[\frac{q_{\max }}{c_{p} T_{1}}=\frac{\left(\mathrm{Ma}_{1}^{2}-1\right)^{2}}{2(k+1) \mathrm{Ma}_{1}^{2}}\\]
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.
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).
An airplane is flying at a flight (or local) Mach number of 0.70 at $10,000 \mathrm{m}$ in the Standard Atmosphere. Find the ground speed (a) if the air is not moving relative to the ground and (b) if the air is moving at $30 \mathrm{km} / \mathrm{hr}$ in the opposite direction from the airplane.
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.
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