Homework 3

(Due on April 29, 2014)

Note:

All numbered problems are from Fundamentals of Fluid Mechanics, Munson et al. 7th Ed.

Copying other peoples work is considered plagiarizing, and it will be treated according tothe university policy.

3.19 When an airplane is flying 200 mph at 5000 ft altitude in a standard atmosphere, the airvelocity at a certain point on the wing is 273 mph relative to the airplane. (a) What suctionpressure is developed on the wing at the point? (b) What is the pressure at the leading edge(astagnation point) of the wing?

3.39 Air flows steadily through a horizontal 4 in. diameter pipe and exits into the atmospherethrough a 3 in. diameter nozzle. The velocity at the nozzle exit is 150 ft/s. Determine thepressure in the pipe if viscous effects are negligible.

3.68 Water flows steadily through the variable area pipe shown in Fig. 1 with negligible viscouseffects. Determine the manometer reading, H, if the flowrate is 0.5 m3/sand the density ofthe manometer fluid is 600 kg/m3.

Figure 1: A variable area pipe.

3.75 Air flows through the device shown in Fig. 2. If the flowrate is large enough, the pressurewithin the constriction will be low enough to draw the water up into the tube. Determinethe flowrate, Q, and the pressure needed at section (1) to draw the water into section (2).Neglect compressibility and viscous effects.

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Figure 2: A water pump.

3.98 When the drain plug is pulled, water flows from a hole in the bottom of a large, opencylindrical tank. Show that if viscous effects are negligible and if the flow is assumed to bequasi-steady, then it takes 3.41 times longer to empty the entire tank than if does to emptythe first half of the tank. Explain why this is so.

3.112 Water flows down the sloping ramp shown in Fig. 3 with negligible viscous effects. Theflow is uniform at section (1) and (2). For the conditions given show that three solutions forthe downstream depth, h2, are obtained by use of the Bernoulli and continuity equations.However, show that only two of these solutions are realistic. Determine these values.

Figure 3: A water flow over the sloping ramp.

4.10 The velocity field of a flow is given by u = V0y/

x2 + y2 and v = V0x/x2 + y2, where

V0 is a constant. Where in the flow field is the speed equal to V0? Determine the equation ofthe streamlines and discuss the various characteristics of this flow.

4.67 Air enters an elbow with a uniform speed of 10 m/s as shown in Fig. 4. At the exit of theelbow, the velocity profile is not uniform. In fact, there is a region of separation or reverseflow. The fixed control volume ABCD coincides with the system at time t = 0. Make a sketchto indicate (a) the system at time t = 0.01 s and (b) the fluid that has entered and exitedthe control volume in that time period.

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Figure 4: An elbow pipe

4.69 Water flows in the braching pipe shown in Fig. 5 with uniform velocity at each inlet andoutlet. The fixed control volume indicated coincides with the system at time t = 20 s. Makea sketch to indicate (a) the boundary of the system at time t = 20.1 s, (b) the fluid thatleft the control volume during that 0.1 s interval, and (c) the fluid that entered the controlvolume during that time interval.

Figure 5: A Y-type pipe

4.73 The wind blows across a field with an approximate velocity profile as shown in Fig. 6. UseEq. 4.16 with the parameter b equals to the velocity to determine the momentum flowrateacross the vertical surface AB, which is of unit depth into the paper.

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Figure 6: A velocity profile of the wind

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