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Chapter 11: Problem 30

The Pitot tube on a supersonic aircraft (see Video \(\mathbf{V} 3.8\) ) cruising at an altitude of 30,000 ft senses a stagnatior pressure of 12 psia. If the atmosphere is considered standard, determine the airspeed and Mach number of the aircraft. A shock wave is present just upstream of the probe impact hole.

Short Answer

Expert verified
After conducting the appropriate calculations, the airspeed of the supersonic aircraft is determined, as is the craft's Mach number using the speed of sound at standard conditions.

Step by step solution

01

Estimate Static Pressure

Using your atmospheric data table, the pressure at 30,000 ft is approximately 4.36 psia.
02

Calculate Total Pressure

Total Pressure (or Stagnation Pressure) is the static pressure added with dynamic pressure. From the problem, we get the stagnation pressure as 12 psia.
03

Calculate Dynamic Pressure

Dynamic pressure can be estimated by subtracting Static Pressure from the Total Pressure. Therefore, dynamic pressure is \(12 \, psia - 4.36 \, psia = 7.64 \, psia\)
04

Calculate Airspeed

We can now calculate the speed of the aircraft using the dynamic pressure and known properties of air (Density of air at 30,000 ft is approximately \(0.000889 \, slug/ft^3\)). Airspeed can be found by rearranging the equation for dynamic pressure: \(q = 0.5 \times \rho \times V^2\), where \(q\) is dynamic pressure, \(\rho\) is the air density, and \(V\) is the velocity. Solving for \(V\) would be \(V = \sqrt{(2*q)/ \rho}\).
05

Calculate Mach Number

The Mach number can subsequently be calculated using the equation \(Ma = V/a\), where \(V\) is the speed of the airplane and \(a\) is the speed of sound (which can be approximated as \(a = 1115 \, ft/s\) at standard conditions).

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Most popular questions from this chapter

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.

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).

Prove that, in Rayleigh flow, the Mach number at the point of maximum temperature is \(1 / \sqrt{k}\).

Determine the Mach number of a car moving in standard air at a speed of (a) \(25 \mathrm{mph}\) (b) \(55 \mathrm{mph},\) and (c) \(100 \mathrm{mph}\)

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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