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Chapter 11: Problem 29

A normal shock occurs in a stream of oxygen. The oxygen flows at \(\mathrm{Ma}=1.8\) and the upstream pressure and temperature are 15 psia and \(85^{\circ} \mathrm{F}\) (a) Calculate the following on the downstream side of the shock: static pressure, stagnation pressure, static temperature, stagnation temperature, static density, and velocity. (b) If the Mach number is doubled to \(3.6,\) what will be the resulting values of the parameters listed in part (b)?

Short Answer

Expert verified
The solution to this problem involves converting the given parameters into SI units, using the normal shock equations for a perfect gas to calculate the downstream temperature, pressure, density and Mach number, determining the stagnation conditions and calculating the downstream velocity. The calculations would then be repeated with the Mach number doubled. The exact values of the downstream properties depend on the specific characteristics of oxygen and the values provided in the normal shock tables.

Step by step solution

01

Convert input values to SI units

Take the given values and convert them into SI units for easier calculation and interpretation. For example, pressure in psia can be converted to Pascals and temperature in Fahrenheit can be converted to Kelvin.
02

Apply the normal shock equations for a perfect gas

Use the already known conditions (upstream Mach number, temperature and pressure) and apply the normal shock equations to derive the downstream pressure (\(P_2\)), temperature (\(T_2\)), density (\(ρ_2\)), and the downstream Mach number (\(Ma_2\)). The equations relate the upstream and downstream variables.
03

Calculate the stagnation properties

Calculate the stagnation pressure (\(P_{02}\)) and temperature (\(T_{02}\)) by using the definition of these quantities. The stagnation pressure and temperature for an adiabatic process are related to the static pressure and temperature by a factor that depends on the specific heats ratio and Mach number.
04

Calculate the downstream velocity

The downstream velocity can be found by using the definition of Mach number and the downstream Mach number obtained in step 2. Velocity of flow is the Mach number times the speed of sound, \(V = Ma \sqrt{γRT_2}\), where \(γ\) is the ratio of specific heats, \(R\) is the gas constant, and \(T_2\) is the downstream temperature.
05

Repeat the calculations for doubled Mach number

Repeat Steps 2, 3, and 4 with the Mach number now doubled to 3.6

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Most popular questions from this chapter

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.

A jet engine is to be designed for an altitude of \(12,000 \mathrm{m}\) where the atmospheric pressure is \(19.3 \mathrm{kPa}\). The jet nozzle has a supersonic exit Mach number and is perfectly expanded. The stagnation pressure and temperature of the gas are 100 kpa and \(600^{\circ} \mathrm{C}\) The flow rate of gas is \(45 \mathrm{kg} / \mathrm{s}\). Calculate the throat area, exit area, and exit velocity. Use \(k=1.4\) and \(R=260 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) for the gas.

Air enters a frictionless, constant area duct with \(\mathrm{Ma}=2.5\) \(T_{0}=20^{\circ} \mathrm{C},\) and \(p_{0}=101 \mathrm{kPa}(\mathrm{abs}) .\) The gas is decelerated by heating until a normal shock occurs where the local Mach number is \(1.3 .\) Downstream of the shock, the subsonic fow is accelerated with heating until it exits with a Mach number of \(0.9 .\) Determine the static temperature and pressure, the stagnation temperature and pressure, and the fluid velocity at the duct entrance, just upstream and downstream of the normal shock, and at the duct exit. Sketch the temperature- entropy diagram for this flow.

An ideal gas flows isentropically through a convergingdiverging nozzle. At a section in the converging portion of the nozzle. \(A_{1}=0.1 \mathrm{m}^{2}, p_{1}=600 \mathrm{kPa}(\mathrm{abs}), T_{1}=20^{\circ} \mathrm{C},\) and \(\mathrm{M} \varepsilon_{1}=0.6 .\) For section (2) in the diverging part of the nozzle, determine \(A_{2}, p_{2},\) and \(T_{2}\) if \(\mathrm{Ma}_{2}=3.0\) and the gas is air.

At a certain point in a pipe, air flows steadily with a velocity of \(150 \mathrm{m} / \mathrm{s}\) and has a static pressure of \(70 \mathrm{kPa}\) and a static temperature of \(4^{\circ} \mathrm{C}\). The flow is adiabatic and frictionless.
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