Introduction and Theoretical Background

# Introduction and Theoretical Background - in the streamwise...

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Introduction and Theoretical Background The purpose of this lab is to show that pressure distribution along a frontal area expressed in dimensionless terms is constant with varying velocity. This is proven by measuring velocity and pressure distributions upstream, around, and in the wake of a cylinder in a wind tunnel. After this data is obtained, the integral equations for mass and momentum are used to estimate the drag on the cylinder. The "drag coefficient", C D , will be used to convert drag force to dimensionless terms. The equation for C D is: C D = F D /(1/2ρA(V^2)) where F D is drag force around the cylinder, ρ is the density of air, V is the velocity of the air, and A is the frontal area of the cylinder. The denominator is the dynamic pressure acting on the frontal area of the cylinder, and the numerator is the drag force or net force
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Unformatted text preview: in the streamwise direction (in our case, the x-direction). The drag force can be determined by integrating the x-component of the pressure force around the cylinder: F D = 2πDL/360∫Pcosθdθ from 0 degrees to 180 degrees, where D and L are the diameter and length of the cylinder, respectively, and Pcosθ is the x-component of the pressure around the cylinder. The integration is from 0 to 180 degrees because the flow about the whole cylinder is assumed symmetric. The integral cannot just be solved as it is because every angle would have to be measured. Instead a trapezoidal approximation will have to be used to approximate the integral in increments of 10 degrees. Also the boundary layer will have to be extrapolated so that the calculations represent a uniform profile....
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