Homework #11 me 363 Fluid Mechanics
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Homework #11 ME 363 - Fluid MechanicsDue Wednesday, April 16, 2008 Fall Semester 2008 1] A student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 2.24 m, and its student designers hope that it can travel fully submerged through water at 0.56 m/s. The water is freshwater (a lake) at T = 15 degrees C. The design team builds a one-eighth scale model to test in their university’s wind tunnel. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel is at 25 degrees C and at atmospheric pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity? 2] This problem builds on problem 1. The students measure the aerodynamic drag on their model submarine in the wind tunnel. They are careful to run the wind tunnel at conditions that ensure similarity with the prototype submarine. Their measured drag force is 2.3 N. Estimate the drag force on the prototype submarine at the conditions given in problem 1. 3] Some students want to visualize flow over a spinning baseball. Their fluids laboratory has a nice water tunnel into which they can inject multicolored dye streaklines, so they decide to test a spinning baseball in the water tunnel. Similarity requires that they match both the Reynolds number and the Strouhal number between their model test and the actual baseball that moves through the air at 80 mph and spins at 300 rpm. Both the air and the water are at 20 degrees C. At what speed should they run the water in the water tunnel, and at what rpm should they spin their baseball?
Problem 1 Solution For a scale model of a submarine being tested in air, we are to calculate the wind tunnel speed required to achieve similarity with the prototype submarine that moves through water at a given speed. Assumptions 1 Compressibility of the air is assumed to be negligible. 2 The wind tunnel walls are far enough away so as to not interfere with the aerodynamic drag on the model sub. 3 The model is geometrically similar to the 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 Similarity is achieved when the Reynolds number of the model is equal to that of the prototype,
We solve Eq. 1 for the unknown wind tunnel speed,
Discussion At this air temperature, the speed of sound is around 346 m/s. Thus the Mach number in the wind tunnel is equal to 61.4/346 = 0.177. This is sufficiently low that the incompressible flow approximation is reasonable. Problem 2 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:
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