fluid mechanics ii (assignment no 1) 2011-15

Fluid Mechanics II (Assignment No. 1) Date Assigned: May 6, 2013 Due Date: May 10, 2013 Q1) A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance 1.3 m from the leading edge is 12 mm. Determine the boundary layer thickness at distances of 0.20, 2.0, and 20 m from the leading edge. Assume laminar flow. Q2) Water flows past a flat plate with an upstream velocity of U = 0.02 m/s. Determine the water velocity a distance of 10 mm from the plate at distances of x = 1.5 m and x = 15m from the leading edge. Q3) Air enters a square duct through a 1-ft opening as is shown in Figure below. Because the boundary layer displacement thickness increases in the direction of flow, it is necessary to increase the cross-sectional size of the duct if a constant U = 2 m/s velocity is to be maintained outside the boundary layer. Plot a graph of the duct size, d , as a function of x for 0 ≤ x ≤10 ft if U is to remain constant. Assume laminar flow. Fig: Q3 Q4) A three-bladed helicopter blade rotates at 200 rpm. If each blade is 12 ft long and 1.5 ft wide, estimate the torque needed to overcome the friction on the blades if they act as flat plates. Q5) A regulation football is 6.78 in. in diameter and weighs 0.91 lb. If its drag coefficient is C D =0.2 determine its deceleration if it has a speed of 20 ft/s at the top of its trajectory. Q6) Repeat the flat-plate momentum integral analysis, using the polynomial profile suggested by K. Pohlhausen in 1921: Does this profile satisfy the boundary conditions of laminar flat-plate flow? Q7) A ship is 125 m long and has a wetted area of 3500 m 2 . Its propellers can deliver a maximum power of 1.1 MW to seawater at 20°C. If all drag is due to friction, estimate the maximum ship speed, in kn. Q8) A ship tows a submerged cylinder, which is 1.5 m in diameter and 22 m long, at 5 m/s in fresh water at 20°C. Estimate the towing power, in kW, required if the cylinder is ( a) parallel and (b) normal to the tow direction. Q9) A 1500-kg automobile uses its drag area C D A = 0.4 m 2 , plus brakes and a parachute, to slow down from 50 m/s. Its brakes apply 5000 N of resistance. Assume sea-level standard air. If the automobile must stop in 8 s, what d iameter parachute is appropriate?

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Fluid Mechanics II (Assignment No. 1)

Date Assigned: May 6, 2013 Due Date: May 10, 2013

Q1) A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance 1.3 m from the leading edge is 12 mm. Determine the boundary layer thickness at distances of 0.20, 2.0, and 20 m from the leading edge. Assume laminar flow. Q2) Water flows past a flat plate with an upstream velocity of U = 0.02 m/s. Determine the water velocity a distance of 10 mm from the plate at distances of x = 1.5 m and x = 15m from the leading edge. Q3) Air enters a square duct through a 1-ft opening as is shown in Figure below. Because the boundary layer displacement thickness increases in the direction of flow, it is necessary to increase the cross-sectional size of the duct if a constant U = 2 m/s velocity is to be maintained outside the boundary layer. Plot a graph of the duct size, d, as a function of x for 0 x 10 ft if U is to remain constant. Assume laminar flow.

Fig: Q3

Q4) A three-bladed helicopter blade rotates at 200 rpm. If each blade is 12 ft long and 1.5 ft wide, estimate the torque needed to overcome the friction on the blades if they act as flat plates. Q5) A regulation football is 6.78 in. in diameter and weighs 0.91 lb. If its drag coefficient is CD =0.2 determine its deceleration if it has a speed of 20 ft/s at the top of its trajectory. Q6) Repeat the flat-plate momentum integral analysis, using the polynomial profile suggested by K. Pohlhausen in 1921:

Does this profile satisfy the boundary conditions of laminar flat-plate flow? Q7) A ship is 125 m long and has a wetted area of 3500 m2. Its propellers can deliver a maximum power of 1.1 MW to seawater at 20C. If all drag is due to friction, estimate the maximum ship speed, in kn. Q8) A ship tows a submerged cylinder, which is 1.5 m in diameter and 22 m long, at 5 m/s in fresh water at 20C. Estimate the towing power, in kW, required if the cylinder is (a) parallel and (b) normal to the tow direction. Q9) A 1500-kg automobile uses its drag area CDA = 0.4 m2, plus brakes and a parachute, to slow down from 50 m/s. Its brakes apply 5000 N of resistance. Assume sea-level standard air. If the automobile must stop in 8 s, what diameter parachute is appropriate?