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Chapter 11: Problem 19

The stagnation pressure in a Mach 2 wind tunnel operating with air is 900 kPa. A 1.0 -cm-diameter sphere positioned in the wind tunnel has a drag coefficient of \(0.95 .\) Calculate the drag force on the sphare.

Short Answer

Expert verified
To solve this problem, one must calculate the cross sectional area of the sphere, compute the dynamic pressure and finally use these values in the drag force equation to obtain the desired result.

Step by step solution

01

Determination of cross-sectional area

First, calculate the cross-sectional area of the sphere: This can be obtained using the sphere's diameter \(D = 1.0\) cm. The cross-sectional area, \(A\), of a sphere is given by \(A = \pi r^2\) where \(r\) is the radius of the sphere = diameter/2 = \(1.0/2\). After converting the radius to meters (since 1cm = 0.01m), compute the area.
02

Calculation of Pressures

Use the given stagnation pressure \(P_0\) = 900 kPa (which should be converted to Pa by multiplying by 1000) and compute the dynamic pressure, which is defined to be half the stagnation pressure, that is \(P = 0.5 P_0\).
03

Calculating the drag force

Now compute the drag force, which is given by the equation \(F_D = C_D \cdot P \cdot A\) where \(C_D\) = 0.95 (drag coefficient), \(P\) is the dynamic pressure calculated in step 2, and \(A\) is the area calculated in step 1.

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Most popular questions from this chapter

A nozzle for a supersonic wind tunnel is designed to achieve a Mach number of \(3.0,\) with a velocity of \(2000 \mathrm{m} / \mathrm{s},\) and a density of \(1.0 \mathrm{kg} / \mathrm{m}^{3}\) in the test section. Find the temperature and pressure in the test section and the upstream stagnation conditions. The fluid is helium.

An aircraft cruises at a Mach number of 2.0 at an altitude of \(15 \mathrm{km} .\) Inlet air is decelerated to a Mach number of 0.4 at the engine compressor inlet. A normal shock occurs in the inlet diffuser upstream of the compressor inlet at a section where the Mach number is \(1.2 .\) For isentropic diffusion, except across the shock, and for standard atmosphere, determine the stagnation temperature and pressure of the air entering the engine compressor.

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