Lab4_Guidelines-Sp'07(2)

# Lab4_Guidelines-Sp'07(2) - ME130L Fluid Mechanics...

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ME130L Fluid Mechanics Laboratory Spring 2007 Background and Guidelines for Lab #4 Drag Measurements for a Cylinder in Cross-flow Objectives: 1. Measure velocity and pressure distributions upstream and in the wake of a cylinder and apply the integral equations for mass and momentum to estimate the drag on the cylinder. 2. Measure the pressure distribution around the cylinder and integrate it to obtain an alternative measure of the drag. 3. Show that the pressure distribution expressed in dimensionless terms is constant with varying velocity and compare these results to published data. 4. Express drag results in terms of dimensionless parameters (specifically drag coefficient and Reynolds number) to generalize your results and permit comparison with published data. Background : Flow over a circular cylinder in cross-flow is one of the classic problems in fluid mechanics. It illustrates a number of important phenomena, including boundary layer effects, flow separation, and vorticity (see Figure 1). These phenomena are characteristic of many other flows as well. Figure 1. Image of the streamlines around a cylinder in cross-flow for Re = 26 (flow visualization using aluminum power on a water surface, by Taneda, J. Phy Soc Jp., 1956) 1

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ME130L Fluid Mechanics Laboratory Spring 2007 The determination of drag on an object by measurement of the velocity and static pressure distributions upstream and in the downstream wake is an excellent example of control volume (integral) analysis. For this experiment these profiles will be made for a cylinder mounted in a wind tunnel, and the data will be used to determine the drag force on the cylinder. Drag on a cylinder can also be calculated by integrating the measured pressure on the surface of the cylinder. The net force in the streamwise direction (x) is called the "drag" force. Drag can be determined by integrating the x-component of the pressure force around the cylinder: Pressure: P = P( θ ) X-component of force due to pressure: d F D = P cos d A = P cos ( Lr d ) = P cos LD d ) where is the angle relative to the flow direction (=0 at the stagnation point), and D and L are the diameter and length of the cylinder, respectively. Integrating around the cylinder: = = 180 0 cos 360 2 cos θθ π d P L D dA P F D Numerical integration of discrete data obtained from experiments is described in the appendix. Integrating from 0º to 180º presumes that the pressure distribution around the cylinder is
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Lab4_Guidelines-Sp'07(2) - ME130L Fluid Mechanics...

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