AE 201 – Spring 2022 Problem Set 7 1. (10 pts) The drag of a race car is to be predicted at a speed of 130 mph. Engineers build a 1/4-scale model of the car to test in a wind tunnel. Determine how fast the engineers should run the wind tunnel to achieve dynamic flow similarity between the wind tunnel model and the prototype car. The aerodynamic drag on the model in the wind tunnel is measured to be 76.5 lb when the wind tunnel is operated at the speed that ensures flow similarity with the prototype car. Determine the drag force on the actual car. Assume all conditions are MSL ISA. 2. (10 pts) Starting from the most general form of the continuity equation and the momentum equation (assume no body forces) in their integral form, explain what these two equations mean and then identify and explain each of the terms. Then show, and explain carefully, how both of these general equations can be simplified for application to problems involving: (i) steady, compressible flows, (ii) incompressible flows, (iii) inviscid, one-dimensional, steady flows. 3. (10 pts) Two pipes of diameters d1 and d2 converge to form a pipe of diameter d. If a liquid flows with a velocity of V1 and V2 in the two pipes, what will be the flow velocity in the third pipe? Hint: Assume one-dimensional flow. 4. (10 pts) Consider the steady flow of a particular gas through a horizontal, converging pipe that has an inlet diameter of 0.22 m and an outlet diameter of 0.16 m. The density of the gas is known to change from 0.91 kg/m3 at the inlet to 0.83 kg/m3 at the outlet. If the inlet flow velocity of the gas is 5.1 m/s, what is its exit velocity? Hint: Assume one-dimensional flow. 5. (10 pts) Consider the flow turning block shown below. A circular jet of water with diameter Dj =10 cm at a velocity Vj = 13 ms−1 enters the block. The water is turned back through 180 degrees by the block and then exits through an orifice with an area of 120 cm2 . First, find the velocity Ve of the water exiting the block. Second, determine the force Fx required to hold the block in place. Hint: Assume one-dimensional flow.
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