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Chapter 6: Problem 46

An open-circuit wind tunnel draws in air from the atmosphere through a well- contoured nozzle. In the test section, where the flow is straight and nearly uniform, a static pressure tap is drilled into the tunnel wall. A manometer connected to the tap shows that static pressure within the tunnel is \(45 \mathrm{mm}\) of water below atmospheric. Assume that the air is incompressible, and at \(25^{\circ} \mathrm{C}, 100 \mathrm{kPa}\) (abs). Calculate the air speed in the wind-tunnel test section.

Short Answer

Expert verified
The air speed in the wind-tunnel test section is approximately \(27 m/s\).

Step by step solution

01

Convert pressure difference to Pascal

Given that the pressure difference is 45 mm of water, we know 1 mm of water is equivalent to 9.80665 Pascals. So, the pressure difference in Pascal is \( 45 \, mm \, H_{2}O \times 9.80665 \, \frac{Pa}{mm \, H_{2}O} \approx 441 \, Pa \).
02

Calculate air density

Air density can be calculated by using the ideal gas law \(蟻 = \frac{P}{RT}\), where \(P = 100 \, kPa = 100000 \, Pa\) is the atmospheric pressure, \(R = 287 \, J/(kg \cdot K)\) is the specific gas constant for dry air, and \(T = 25^{\circ}C + 273.15 = 298.15 K\) is the absolute temperature. Substitute these values into the equation and calculate to find \(蟻 \approx 1.184 \, kg/m^3\).
03

Calculate air speed

Now, apply Bernoulli's theorem on a streamline from the free stream outside the wind tunnel to the test section, \(P_{0} = P_{1} + \frac{1}{2} \rho v^{2}\). Rearranging the equation we get, \(v = \sqrt{\frac{2 (P_{0}-P_{1})}{\rho}}\), substitute \(P_{0} - P_{1} = 441 Pa\) and \(蟻 = 1.184 kg/m^3\) into the equation, therefore, the air speed \(v \approx 27 m/s\).

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Most popular questions from this chapter

Calculate the dynamic pressure that corresponds to a speed of $100 \mathrm{km} / \mathrm{hr}$ in standard air. Express your answer in millimeters of water.

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The inlet contraction and test section of a laboratory wind tunnel are shown. The air speed in the test section is \(U=50 \mathrm{m} / \mathrm{s} .\) A total- head tube pointed upstream indicates that the stagnation pressure on the test section centerline is \(10 \mathrm{mm}\) of water below atmospheric. The laboratory is maintained at atmospheric pressure and a temperature of \(-5^{\circ} \mathrm{C}\) Evaluate the dynamic pressure on the centerline of the wind tunnel test section. Compute the static pressure at the same point. Qualitatively compare the static pressure at the tunnel wall with that at the centerline. Explain why the two may not be identical.
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