331 CEE Fluid Mechanics: Prelim 1 July 21, 1998 - 11:30 AM -12:45 PM Closed book, one 8.5 x 11 summary sheet
May the time you spent preparing for this exam pay off. Note that there are constants and equations on the last sheet of the exam. Read each problem carefully before beginning to work on the answer! Make sure you answer each part of each question. Solve all problems using symbols and then substitute numerical values (with units) as a last step. Show your work and underline your final answers. 1) A water column is used to measure the barometric pressure. The water column is outside and the temperature of the water varies with the outdoor temperature. The water barometer was created by filling the tube with pure water and then inverting it. A) (20 points) Calculate the barometric pressure (in kPa) when the outdoor temperature is 35C (water = 994 kg/m3) and R is 9.55 m. (98.7 kPa) B) (5 points) Express your answer (Hg = 13,600 kg/m3). (741 mm Hg) in mm Hg
R
8000 7000 6000 5000 4000 3000 2000 1000 0 0 10 20 30 Temperature (C) 40
Vapor pressure (Pa)
2) An automatic gate is installed in an irrigation channel. The angle is 30 and the gate is 2 m wide. A) (20 points) Determine the pivot location "a" of the rectangular gate so that it will open when the liquid surface is as shown. (a = 0.4445 m) B) (15 points) What is the resultant force acting on the gate? (F = 34 kN) C) (5 points) Would the water surface need to be or raised lowered to keep the gate closed?
2m 1m
30 a
3) A scoop attached to a locomotive is used to lift water from a stationary water tank next to the train tracks into a water tank on the train. The scoop pipe is 10 cm in diameter and elevates the water 3 m. Consider the locomotive stationary and the water moving toward the scoop to reduce to a steady-flow situation.
Q = 4 L/s d = 10 cm 3m Vscoop
A) (5 points) Draw several streamlines in the left half of the stationary water tank stationary water tank (use the scoop as your frame of reference) including the streamlines that attach to the submerged horizontal section of the scoop. B) (10 points) Use the streamlines to help you draw a control volume and clearly label the control surfaces. C) (20 points) How fast must the locomotive be moving (Vscoop) to get a flow of 4 L/s if the frictional losses in t...