Homework 6 solutions

Homework 6 solutions - Homework 6 Due Wednesday, September...

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Homework 6 – Due Wednesday, September 29 th 1. Consider the chip we discussed in class. We used a correlation such that Nu x = 0.04 Re x 0.85 Pr 1/3 . We were able to use this local correlation not because the chip was so small (4 mm X 4 mm) but that the object was not far from the leading edge (120 mm in) , i.e. the L is 120 mm. a) Find an average coefficient and see if the assumption was valid. (9 pts) b) Calculate the local and average coefficient if the chip is placed 600 mm from the leading edge. Would it be safe to assume they can be used interchangeably? (11 pts) a)
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2. A fan can provide air speeds up to 40 m/s is used in a wind tunnel with air at 25 o C. a) What is the minimum plate length that can be used to study boundary layer behavior up to Reynolds numbers of 10 8 ? (5 pts) b) At what distance will transition occur? (5 pts) c) Using a spreadsheet, generate lengths between .01 and .2 meters and calculate the Reynolds numbers for these lengths. Knowing the Re x,c and the x c , see if there’s a relationship between the two lengths and the two Re’s. Use this knowledge to find the x c for a plate that is 10 meters long with a fan speed of 20 m/ s. (5 pts) a) 1 X 10 8 = VL/ ν L = 1 X 10 8 * 15.89 X 10 -6 /40 = 39.7 m b) L = 5 X 10 5 *15.89 X 10 -6 /40 = 0.2 m c) x c /L = Re c /Re L x c = 10*(5 X 10 5 /1.26 X 10 7 ) = 0.397 m u 40 L=Re(nu/u) T 298 a L 39.73 nu 1.59E-05 b L 0.20 Re L/xc Re/Rec 0.01 2.52E+0 4 0.050346 0.050346 0.02 5.03E+0 4 0.100692 0.100692 0.03 7.55E+0 4 0.151038 0.151038 0.04 1.01E+0 5 0.201385 0.201385 L/xc=Re/Rec 0.05 1.26E+0 5 0.251731 0.251731 0.06 1.51E+0 5 0.302077 0.302077 0.07 1.76E+0 5 0.352423 0.352423 Rex 1.26 E+0 7 0.08 2.01E+0 5 0.402769 0.402769 xc 3.97 E-01 0.09 2.27E+0 5 0.453115 0.453115 0.1 2.52E+0 5 0.503461 0.503461 0.11 2.77E+0 5 0.553807 0.553807 0.12 3.02E+0 5 0.604154 0.604154
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0.13 3.27E+0 5 0.6545 0.6545 0.14 3.52E+0 5 0.704846 0.704846 0.15 3.78E+0 5 0.755192 0.755192 0.16 4.03E+0 5 0.805538 0.805538 0.17 4.28E+0 5 0.855884 0.855884 0.18 4.53E+0 5 0.90623 0.90623 0.19 4.78E+0 5 0.956576 0.956576 0.2 5.03E+0 5 1.006923 1.006923 3. Water at 50 o C and a velocity of 10 m/s flows over both surfaces of a 1 m long flat plat maintained at 20 o C. Find: a) the velocity and thermal boundary layer thicknesses at the trailing edge ( 5pts) b) the local heat flux and surface stress at the trailing edge (10 pts) c) the total drag force and heat transfer per unit width of the plate (10 pts) d) Plot the boundary layer thicknesses and local values of the surface shear stress, convection coefficient (15 pts) – be generous with this one – you will get a lot of different answers.
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Homework 6 solutions - Homework 6 Due Wednesday, September...

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