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Chapter 11: Problem 25

Sound waves are very small-amplitude pressure pulses that travel at the "speed of sound." Do very large-amplitude waves such as a blast wave caused by an explosion (see Video \(\vee 11.8\) ) travel less than, equal to, or greater than the speed of sound? Explain.

Short Answer

Expert verified
A blast wave caused by an explosion, which is a very large-amplitude wave, can travel at speeds greater than the normal speed of sound. This happens as the intense energy from the blast wave alters and heats up the medium, thus increasing the local speed of sound.

Step by step solution

01

Understanding the nature of sound waves

Sound waves, whether very small or very large in amplitude, are essentially pressure waves that transfer energy through a medium. They move at the speed of sound, which is a specific characteristic of the medium through which they travel.
02

Considering the effect of amplitude on wave speed

Generally, the amplitude of a wave, which refers to the wave's strength or power does not have a direct effect on its speed according to wave theory. A blast wave from an explosion is an example of a high amplitude wave, but this doesn't mean that it automatically travels at a speed greater than the speed of sound.
03

Factoring in the conditions of a blast wave

However, a blast wave is a unique case, as it has sufficient amplitude and energy to alter the conditions of the medium through which it travels. This can subsequently cause it to move faster than the typical speed of sound in that medium. This is due to the fact that the blast wave heats up the air as it travels, increasing the local speed of sound.

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Most popular questions from this chapter

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?

The gas entering a rocket nozzle has a stagnation pressure of \(1500 \mathrm{kPa}\) and a stagnation temperature of \(3000^{\circ} \mathrm{C}\). The rocket is traveling in the still Standard Atmosphere at \(30,000 \mathrm{m}\). Find the throat and exit area for a flow rate of \(10 \mathrm{kg} / \mathrm{s}\). Assume \(k=1.35, R=\) \(287.0 \mathrm{N} \cdot \mathrm{m} / \mathrm{kg} \cdot \mathrm{K} .\) The gas is perfectly, expanded to the ambient pressure.

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.

An air heater in a large coal-fired steam generator heats fresh air entering the steam generator by cooling flue gas leaving the steam generator. One million lbm/hr of air at \(100^{\circ} \mathrm{F}\) and 1.1 million lbm/hr of flue gas at \(720^{\circ} \mathrm{F}\) enters the air heater. The flue gas leaves at \(310^{\circ} \mathrm{F}\). Flue gas has \(c_{p}=0.26 \mathrm{Btu} / \mathrm{lbm}^{\circ} \mathrm{F}\) and \(k=1.39 .\) Pressure changes are small and may be neglected. Calculate the temperature of the air leaving the air heater and the total entropy change for the process.

Supersonic airflow enters an adiabatic, constant area (inside diameter \(=1 \mathrm{ft}\) ) 30 -ft-long pipe with \(\mathrm{Ma}_{1}=3.0 .\) The pipe friction factor is estimated to be \(0.02 .\) What ratio of pipe exit pressure to pipe inlet stagnation pressure would result in a normal shock wave standing at (a) \(x=5\) ft, or \((\mathbf{b}) x=10 \mathrm{ft},\) where \(x\) is the distance downstream from the pipe entrance? Determine also the duct exit Mach number and sketch the temperature-entropy diagram for each situation.
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