EFM HW 5 Due101717 liu ti li xxue PDF

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sd01632100: Engineering Fluid Mechanics Homework#5 Due: Tuesday, October 17th, 2017 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). 1. A large tank open to the atmosphere is filled with water to a height of 5 m from the outlet tap. When the tap (near the bottom of the tank) opens, water flows out from the smooth and rounded outlet. Determine the maximum water velocity at the outlet. (10 points)

2. The water level in a tank is 15 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the pressure above the water surface is 3 atm gage. The system is at sea level. Determine the maximum height to which the water stream could rise. (10 points).

3. In a hydroelectric power plant, water enters the turbine nozzle at 800 kPa absolute pressure with a low velocity. If the nozzle outlet is exposed to atmospheric pressure of 100 kPa, determine the maximum velocity to which water can be accelerated by the nozzle before striking the turbine blades. ( 8 points) 4. To model the velocity distribution in the curved inlet section of a wind tunnel, the radius of curvature of the streamlines is expressed as R=LR0/2n. As a first approximation assume the air speed along each 1/3

streamline is V=20 m/s. Evaluate the pressure change from n=0 to the tunnel wall at n=L/2, if L=150 mm and R0=0.6 m. (12 points)

5. A Pitot-static probe connected to a water manometer is used to measure the velocity of air. If the deflection (the vertical distance between the fluid levels in the two arms) is 7.3 cm, determine the air velocity. Take the density of air to be 1.25 kg/m 3. (10 points)

6. Consider steady, incompressible, two-dimensional flow through a converging duct as shown. A simple approximate velocity field for this flow is: V  (u, v)  (U0  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. Generate an analytical expression for the flow streamlines. II. For the case of U0=3.56 ft/s and b=7.66 s-1, plot several steam lines from x=0 ft to 5 ft and y=-2 ft to y=2 ft. Be sure to show the direction of the streamlines. (16 points)

7. In addition to the customary horizontal velocity components of the air in the atmosphere (the “wind”), there often are vertical air currents (thermals) caused by buoyant effects due to uneven heating of the air 2/3

as indicated in the figure. Assume that the velocity field in a certain region can be approximated by u = u0, v = v0[1-y/h] for 0< y h. Plot the streamlines that pass through the origins for values of u0/v0 = 0.5, 1, and 2. Hint: plot streamlines on an x/h. and y/h coordinate frame. (14 points)

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