# Saet3a - FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 3 BOUNDARY LAYERS SELF ASSESSMENT EXERCISE 1 1 A smooth thin plate 5 m long and 1 m wide is

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FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 3 – BOUNDARY LAYERS SELF ASSESSMENT EXERCISE 1 1. A smooth thin plate 5 m long and 1 m wide is placed in an air stream moving at 3 m/s with its length parallel with the flow. Calculate the drag force on each side of the plate. The density of the air is 1.2 kg/m 3 and the kinematic viscosity is 1.6 x 10 -5 m 2 /s. R ex = u L/ ν = 3 x 5/1.6 x 10 -5 = 937.5 x 10 3 C DF = 0.074 R ex -1/5 = 4.729 x 10 -3 Dynamic Pressure = ρ u o 2 /2 = 1.2 x 3 2 /2 = 5.4 Pa τ w = C DF x dyn press = 0.0255 Pa R = τ w x A = 0.0255 x 5 = 0.128 N 2. A pipe bore diameter D and length L has fully developed laminar flow throughout the entire length with a centre line velocity u o . Given that the drag coefficient is given as C Df = 16/Re where µ ρ = D u Re o , show that the drag force on the inside of the pipe is given as R=8 πµ u o L and hence the pressure loss in the pipe due to skin friction is p L = 32 µ u o L/D 2 C DF = 16/R e R = τ w x ρ u o 2 /2 = C DF x ( ρ u o 2 /2) x A R = (16/R e )( ρ u o 2 /2) A R = (16μ/ ρ u o D)( ρ u o 2 /2) π DL R = (16 μ u o π L/2) = 8 π μ u o L p L = R/A = 8 π μ u o L /( π D 2 /4) = 32 μ u o L/D 2 SELF ASSESSMENT EXERCISE No. 2 1. Calculate the drag force for a cylindrical chimney 0.9 m diameter and 50 m tall in a wind blowing at 30 m/s given that the drag coefficient is 0.8. The density of the air is 1.2 kg/m 3 . C

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## This note was uploaded on 09/06/2011 for the course ASE 13180 taught by Professor Goldstein during the Spring '10 term at University of Texas at Austin.

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Saet3a - FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 3 BOUNDARY LAYERS SELF ASSESSMENT EXERCISE 1 1 A smooth thin plate 5 m long and 1 m wide is

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