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AE 2020 Homework Set #2 Due on Thursday February 4, 2008 1. In a two-dimensional low speed flow experiment, the velocity field was measured and curve fitted as: V 3x 3y i j x2 y2 x2 y2 Verify if this velocity field satisfies the continuity equation. Hint: Identify the u- and v- components. Determine whether u/x + v/y adds up to zero. 2. 10 ft Consider the cross section of a sluice gate, which is a device for controlling the flow of water in channels. Determine the force on the gate per unit width of the gate. Inflow velocity = 5 ft/sec V=? 3 ft Hint: think of each line as a surface, with the length given above, and 1 foot of depth in the direction normal to the plane of the paper. The hydrostatic gauge pressure field p equals gh. That is, the gauge pressure at any point in the flow will linearly vary with the depth of the water, h. Use the average values of the pressure (at half-depth) for the pressure forces. Ans: V =16.667 ft/sec, Force in the x- direction on the gate = 1708 lb per foot of width in the direction normal to the plane of the paper. 3. Consider the flow of water through the nozzle-elbow assembly shown below. The water issues out as a free jet from the nozzle at atmospheric pressure. What is the force along the x- direction on the nozzle assembly? Jet Exit diameter= 0.15 m Inflow Velocity= 1.5 m./sec Diameter of pipe at inflow = 0.3 m Gauge Pressure = 100,000 Pascal Ans: 7864 N 4. A pipe tapers from a diameter of 0.5 m at the inlet to a diameter of 0.25 m at the outlet, and turns by an angle of 45 degrees. The gauge pressure at the inlet and the outlet are 40000 N/m2 and 23000 N/m2, respectively. The pipe carries oil, with a density of 850 kg/ m3, at a rate of 0.45 m3/sec. Compute the magnitude and direction of the force acting on the turn. 45 deg Ans: 6362 N at a direction 31 degrees relative to the inflow.