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Chapter 7: Problem 96

A 1: 16 model of a bus is tested in a wind tunnel in standard air. The model is \(152 \mathrm{mm}\) wide, \(200 \mathrm{mm}\) high, and \(762 \mathrm{mm}\) long. The measured drag force at \(26.5 \mathrm{m} / \mathrm{s}\) wind speed is 6.09 N. The longitudinal pressure gradient in the wind tunnel test section is \(-11.8 \mathrm{N} / \mathrm{m}^{2} / \mathrm{m}\). Estimate the correction that should be made to the measured drag force to correct for horizontal buoyancy caused by the pressure gradient in the test section. Calculate the drag coefficient for the model. Evaluate the aerodynamic drag force on the prototype at \(100 \mathrm{km} / \mathrm{hr}\) on a calm day.

Short Answer

Expert verified
The corrected drag force on the test model is 7.46N. The drag coefficient for the model is 0.78. The aerodynamic drag force on the actual bus at 100km/hr on a calm day would be approximately 10584N.

Step by step solution

01

Calculate scale factor

The scale ratio is given as 1:16 for the model and the prototype. So, the scale factor is 16.
02

Calculate pressure gradient and buoyancy force

The pressure gradient in the tunnel is given as -11.8 N/m^2/m. Integrated over the length (l) of the model, it gives a pressure difference 螖p = \(-11.8 \mathrm{N} / \mathrm{m}^{2} / \mathrm{m}\) * 0.762 m = -8.99 N/m^2. The area (A) over which this pressure acts is the side area of the bus, A = 200mm*762mm = 0.152 m^2. The horizontal buoyancy force due to pressure gradient F_B can be calculated using the equation F_B = 螖p*A = -8.99 N/m^2 * 0.152 m^2 = -1.37 N.
03

Calculate corrected drag force

The measured drag force is influenced by the horizontal buoyancy caused by the pressure gradient. The corrected drag force F_D can be calculated by subtracting the buoyancy force from the measured force: F_D = F_measured - F_B = 6.09 N - (-1.37 N) = 7.46 N.
04

Calculate the drag coefficient for the model

The drag coefficient C_D can be computed with the corrected drag force, the wind speed and the air density using the formula: C_D = 2*F_D / (蟻*V^2*A). Standard air density 蟻 can be approximated as 1.225 kg/m^3 at sea level. Substituting the known values, we get C_D = 2*7.46 N / (1.225 kg/m^3 * (26.5 m/s)^2 * 0.152 m^2) = 0.78.
05

Evaluate the aerodynamic drag force on the prototype

At the prototype scale, the aerodynamic drag force F_D can be calculated using the drag coefficient, wind speed, air density, and prototype area (which is 16^2 = 256 times the model area). We can compute it as: F_D = 0.5*C_D*蟻*V^2*A = 0.5*0.78 * 1.225 kg/m^3 * (100 km/hr to m/s)^2 * 256 * 0.152 m^2 = 10584 N approximately.

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