EFM HW 3 Due101017 Solution PDF

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sd01632100: Engineering Fluid Mechanics Homework#3 Due: Wednesday, September 28th, 2016 Instructions:  Homework is due at the beginning of the class on the date indicated above.  Solutions must be presented according to the “problem solving guideline” handed out during the first class (also available in syllabus).

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1. A stationary probe is placed in a fluid flow and measures pressure and temperature as functions of time at one location in the flow. Is this Lagrangian or Eulerian measurement? Explain. (5 points)

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2. A pitot-static probe can often be seen protruding from the underside of an airplane. As the airplane flies, the probe measures relative wind speed. Is this Lagarngian or Eulerian approach? Explain. (5 points).

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3. Consider steady, incompressible, two-dimensional flow through a converging duct as shown. A simple approximate velocity field for this flow is: V (u, v) (U 0  bx)i  byj

where U0 is the horizontal speed at x=0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field.

I. Calculate the material acceleration for fluid particles passing through the ducts. Give your answer in two ways: (1) as acceleration components ax and ay and (2) as acceleration vector a . II. If the pressure field for this flow is given by: p  p0 

 2U bx  b(x  y)  2 0

where p0 is the pressure at x=0. Generate an expression for the rate of change of pressure following a 4/10

fluid particle. (20 points)

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4. A smoking lounge is to accommodate 15 heavy smokers. The minimum fresh air required for smoking lounges is specified to be 30 L/s per person (ASHRAE, standard 62,1989). Determine the minimum required flow rate of fresh air that needs to be supplied to the lounge, and the minimum diameter of the duct if the air velocity is not to exceed 8 m/s. (10 points)

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5. A 1 m3 rigid tank initially contains air whose density is 1.18 kg/m3. The tank is connected to a high pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 7.20 kg/m3. Determine the mass of air that has entered the tank. (5 points)

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6. Water enters a large tank of diameter DT steadily at a mass flow rate of

 in m

. An orifice at the bottom

with diameter D0 allows water to escape. The orifice has a rounded entrance, so the frictional losses are negligible. If the tank is initially empty, obtain a relationship for water height z as a function of time. (17 points)

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7. The characteristic shape of downtown Pittsburgh is a triangular tract carved over time by the confluence of the "Allegheny" and "Monogahela" rivers, thus giving rise to "Ohio" river. At a location downstream from the junction of "Allegheny" and "Monogahela" rivers, before the two streams completely merge, the non-uniform velocity profile of the "Ohio" river is as shown. Determine the value of V. (13 points)

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