HW_17_Soln

HW_17_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 17...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 17 Due Wed 8 Oct 2008 Problem 17-1 The radius of curvature of the streamlines in the converging inlet to a water channel are approximated as R = LR 0 /2y and the velocity on each streamline is uniform at V = 10 m/s . Find the pressure change from the centerline, y = 0 , to the channel wall, y = L/ 2, where L= 200 mm, and R 0 = 0.5 m . Solution: Given : Radius of curvature of SL’s at inlet Speed along each V = 10 L = 0.1, R = 0.5 Find : pressure difference from centerline to wall Assumptions : Steady, frictionless flow, incompressible, no body forces, constant velocity along each streamline. Analysis : Normal momentum equation: R V n p 2 ρ = Apply equation at inlet plane: L R V y R V y p n p 0 2 2 2 = = - = Separate variables and integrate: dy L R V y dp 0 2 2 - = or 2 0 2 0 y L R V p p - = - Evaluate at outer wall: 2 0 2 0 2 / / 9950 4 m N R L V p p p L - = - = - = Α (Note: Minus sign implies pressure is lower on the wall than on the centerline.) Problem 17-2
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HW_17_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 17...

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