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BME259 Problem Set 4 Solutions

BME259 Problem Set 4 Solutions - BME/CHE 259 Problem Set#4...

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BME/CHE 259 Problem Set #4 Solutions 1. Problem 3.1 Derive the relationship between the Strouhal number and the Womersley number. Solution The Strouhal number = and the Womersley number = . Begin with the Womersley number and multiply top and bottom by V x , Using T=1/w and L=2R,
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2. Problem 3.2 Using Poiseuille's law (Equation 2.7.44), show that the friction factor defined in Equation (3.5.6) for laminar flow in a cylindrical tube is simply 16/Re. Solution Equation 2.7.45 Equation 3.5.6 The friction factor for a cylindrical tube is defined by Equation 3.5.6 above. Inserting Equation 2.7.42 into Equation 2.7.44 , Gives . Insert into Equation 2.7.45 give us Rearranging and solving for P Substitute the above equation into Eq. 3.5.6 gives,
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3. Problem 3.11 Considerable insight into a flow problem can be gained soley from the continuity equation. Consider laminar flow over a flat plate, as shown in Figure 3.23. Fluid approaches the plate with a uniform velocity U. When the fluid is in contact with the surface, flow in the x-direction
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