Lab 4 - Introduction and Theoretical Background The purpose...

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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 )) For 24.382 m/s The Reynolds Number is 3.1656 x 10 4 (Calculation show in Figure 1) C D ~1.5 (from figure 2 in lab handout) C D =1.50758 (from Figure 1 in lab write-up) 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 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. The pressure around the cylinder is expected to decrease until just before 90 degrees. This is because the mass flow between any two stream lines is a constant since the density and mass flow are the same; thus as the area between two streamlines goes down (from 0 to 90 degrees), the velocity must increase. At just before 90 degrees gage static pressure is at its lowest eg. -971Pa, this static pressure is what is causing the air to move there for when the gage
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This note was uploaded on 04/07/2008 for the course ME 130L taught by Professor Fredthomas during the Spring '08 term at University of Texas at Austin.

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Lab 4 - Introduction and Theoretical Background The purpose...

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