pqe fluid mechanics 2009

Mech

Mech. Eng. Ph.D. Preliminary Qualifying Examination

January 22, 2009Fluid Mechanics

This is one of five problems. You are required to do four out of five problems. Clearly indicate which four problems you are selecting. Show all work on the exam sheets provided and write your student number on each sheet. Do not write your name on any sheet.

Student Number ______________________________________________________

1. Consider the low-speed flow of air between parallel disks as shown. Assume that the flow is incompressible and inviscid, and that the velocity is purely radial and uniform at any section. The flow speed is V = 15 m/s at R = 75 mm. Simplify the continuity equation to a form applicable to this flow field. Show that a general expression for the velocity field is for. Calculate the acceleration of a fluid particle at the locations.

Fig. 1




Student Number ______________________________________________________

2. Consider steady laminar flow in a parallel-plate device where one wall is lined with endothelial cells to demonstrate elongated cell alignment with substantial shear flow. Given , and as well as measured , calculate the operational conditions, i.e., associated Reynolds numbers and entrance length (for cell placement in the fully-developed flow region). (Assume Poiseuille-type flow.)

Fig. 2




Student Number ______________________________________________________

3. The pressure drop in a Venturi meter varies only with the fluid density, pipe approach velocity, and diameter ratio of the meter. A model venture meter tested in water at 20oC shows a 5 kPa drop when the approach velocity is 4 m/s. A geometrically similar prototype meter is used to measure gasoline (density 680 kg/m3) at a flow rate of 9 m3/min. If the prototype pressure gauge is most accurate at 15kPa, what should the upstream pipe diameter be?Solution:Given: P=fn(, U, d/D)

Using Buckingham Pi theorem to obtain the useful relationship of

non-dimensional pressure drop: P/(U2)= fn(d/D)

For Water model: 5000/(998. 42 ) = 0.313For Gasoline prototype: 15000/(680 . U2 ) = 0.313 Solve for U

( U = 8.39 m/s

By definition, Flow rate : Q =U A= U (D2 )/4, and is given as 9/60 m3/s;

Solve for D , obtain ( D=0.151 m




Student Number ______________________________________________________

4. The drag force of a bullet-shaped device may be measured using a wind tunnel. The tunnel is round with a diameter of 1 m, the pressure at section 1 is 1.5 kPa gage, the pressure at section 2 is 1.0 kPa gage, and air density is 1.0 kg/m^3. At the inlet, the velocity is uniform with a magnitude of 30 m/s. At the exit, the velocity varies linearly as shown in the sketch. Determine the drag force on the device and support vanes. Neglect viscous resistance at the wall, and assume pressure is uniform across sections 1 and 2.

Fig. 4




Student Number ______________________________________________________5. A hydroelectric power plant in Fig. 5 takes in 30m3/s of water through its turbines and discharges it at V2 = 2 m/s at atmospheric pressure. The head loss in the turbine and penstock system is hf= 20 m.

a. Calculate the exit area

b. Estimate the power extracted by the turbine in megawatts.

Fig. 5

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