FLUID MECHANICS WORCESTER POLYTECHNIC INSTITUTE ES3004 HOMEWORK #2 Due Wednesday May 31 by 11:59 pm on Canvas Study Chapter 5.1 Problems: (4 points each, unless otherwise noted) 1. Problem 5.4 2. Problem 1.44 3. Problem 5.8 4. Problem 5.17 5. A uniform flow with velocity U enters a channel of height 2h and width W (into the paper). The velocity profile at the pipe outlet is given by 2 y u? U (1? ) 0 2 h a) Find the ratio U /U. 0 b) Explain why the magnitude of U /U (e.g., is it less than or greater than 1) makes sense 0 physically. 6. A uniform flow with velocity U enters a circular pipe of height R. The velocity profile at the pipe outlet is given by 2 r u? U (1? ) 0 2 R a) Find the ratio U /U. 0 7. Problem XXXXXXXXXXA conical funnel of half-angle ? is filled to some initial height h with a fluid. At time t = 0 the 0 drain plug is removed and the fluid drains through a hole (with area a) in the bottom of the funnel. Assume that the drain hole area is small compared to the fluid surface area. a. Fill in the following table The dependent variable in this problem is the drain time , t D Independent If the Your Analysis Does Your Variable Independent Prediction Prediction: Prediction Variable From Match the Physical Analysis (with all other Intuition: Prediction: parameters Does t held constant) D increase (?) or decrease (?) ? Funnel half-? angle ?? Initial fluid ? height h 0 Drain hole area ? a Gravitational ? Acceleration g b) Find an expression for the fluid height h(t) as a function of time. Hint: The way in which this problem differs from the draining tank in class is that the tank area is no longer constant with height. You must find an equation for the tank area A = f(h). c) Find an expression for the funnel drain time. h L ?? h = 0
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