SPRING 2010 – CE 341 – INTRODUCTION TO FLUIDS

TRADITIONAL HOMEWORK #3 – DUE WEDS, MARCH 24TH, 2010


⦁    Bernouilli’s Equation (TO RECEIVE CREDIT, ANSWERS MUST BE TYPED IN TIMES NEW ROMAN AND WRITTEN IN COMPLETE SENTENCES – 20 pts TOTAL):
⦁    What law do we derive Bernoulli’s Equation from?  Why? (3 PTS)
⦁    From what law do we derive Qin = Qout from? Why?  (3 PTS)
⦁    Write out and explain the physical meaning of each term in Bernoulli’s Equation. (4 PTS)
⦁    What assumptions is Bernoulli’s Equation based on?  Explain.  (5 PTS)
⦁    Explain the restrictions of Bernoulli’s equation. (5 PTS)  (Hint: use section 3.8 in textbook for help).

⦁    The figure shows a 10-cm diameter, horizontal pipeline with two piezometers installed 3 m apart.  Under laminar flow of lubricating oil (specific gravity = 0.92 and viscosity = 3.8x10-1 Pa-s), the difference in piezometer readings is 12 cm.  Find the flow rate (m3/min) under this condition and clearly state all assumptions.
 

⦁    The figure shows a horizontal pipeline with a sudden enlargement. The energy grade line and the hydraulic grade line under a certain flow of an incompressible fluid of specific weight 10 kN/m3 are also shown. Find the pressure change due to the enlargement and clearly state all assumptions in this problem.

 
⦁    A 5-cm diameter pipeline is delivering water from a storage tank to an open canal. The water level in the storage tank can be assumed to be at a constant height of 12 m above the discharge point. Ignoring all losses, (i) draw a clearly labeled schematic of the problem and (ii) find the discharge in m3/min under these conditions.

⦁    At a certain section in a pipeline, a reducer is used to reduce the diameter from 2D gradually to diameter D. When an incompressible fluid flows through this pipeline, the velocity is U1 in the first section and U2 in the second section. Please perform the following (i) draw a schematic of the problem, and (ii) find the relationship between U1 and U2.

⦁    An inclined-tube manometer is being used as shown to measure the pressure in a pressurized tank. The tank is partially filled to a depth of 20 cm with a fluid of specific gravity = 0.78. The specific gravity of the manometric gage fluid is 3.5. Find the gage pressure in the headspace in kPa when h = 8 cm.
30 degree angle
 

 Water at 170°F flows horizontally through the constriction of the figure when the atmospheric pressure is 28.2 inHg.  Neglecting head loss, find the flow rate at which cavitation begins.




⦁   
 (10 PTS): Refer to the figure.  Find the maximum value for b if a = 3.5 ft.  Assume friction is negligible and the minimum pressure allowable in the siphon is a vacuum of –32.8 ft of water. 

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