Homework #11 me 363 Fluid Mechanics
Solution We are to estimate the drag on a prototype submarine in water, based on aerodynamic drag measurements performed in a wind tunnel. Assumptions
Download 301.47 Kb.
|
1 2
Solution We are to estimate the drag on a prototype submarine in water, based on aerodynamic drag measurements performed in a wind tunnel. Assumptions 1 The model is geometrically similar. 2 The wind tunnel is run at conditions which ensure similarity between model and prototype. Properties For water at T = 15oC and atmospheric pressure, = 999.1 kg/m3 and = 1.138 10-3 kg/ms. For air at T = 25oC and atmospheric pressure, = 1.184 kg/m3 and = 1.849 10-5 kg/ms. Analysis Since the Reynolds numbers have been matched, the nondimensionalized drag coefficient of the model equals that of the prototype,
We solve Eq. 1 for the unknown aerodynamic drag force on the prototype, FD,p,
where we have used the wind tunnel speed calculated in Problem 7-36. Discussion Although the prototype moves at a much slower speed than the model, the density of water is much higher than that of air, and the prototype is eight times larger than the model. When all of these factors are combined, the drag force on the prototype is much larger than that on the model. Problem 3 Solution We are to calculate the speed and angular velocity (rpm) of a spinning baseball in a water channel such that flow conditions are dynamically similar to that of the actual baseball moving and spinning in air. Properties For air at T = 20oC and atmospheric pressure, = 1.204 kg/m3 and = 1.825 10-5 kg/ms. For water at T = 20oC and atmospheric pressure, = 998.0 kg/m3 and = 1.002 10-3 kg/ms. Analysis The model (in the water) and the prototype (in the air) are actually the same baseball, so their characteristic lengths are equal, Lm = Lp. We match Reynolds number,
and solve for the required water tunnel speed for the model tests, Vm,
We also match Strouhal numbers, recognizing that  is proportional to f,
from which we solve for the required spin rate in the water tunnel,
Discussion Because of the difference in fluid properties between air and water, the required water tunnel speed is much lower than that in air. In addition, the spin rate is much lower, making flow visualization easier. Directory: ~ssanders -> me 363 -> homework solutions with problem statements -> spring 2008 spring 2008 -> Homework #10 me 363 Fluid Mechanics homework solutions with problem statements -> Homework #10 me 363 Fluid Mechanics Download 301.47 Kb. Share with your friends:
|
1 2