Sample 1 Test #3 for CEE-3500 (borrowed from Dr. Rahmeyer’s notes)
#1. For Reynolds similitude, derive the Force ratio in terms of only geometric and fluid
properties (i.e., no velocity).
#2. Given a flow of 100,000 cfs over a sharp edged weir that is 20 feet wide and 10 feet
high. A model is built of the weir so that the model flow is 50 cfs. How wide and tall is
the model?
#3. Given a viscous flow in a water tunnel around a cylinder of length L and diameter D.
The velocity V is measured in the water tunnel along with the drag force Fd on the
cylinder. Derive the Π(Pi) term from dimensional analysis that includes the variables F
and D.
#4. Given an upstream reservoir that has its water surface elevation at 80 feet. A
downstream reservoir has its water surface at an elevation of 40 feet. A 12” diameter
pipe connects the two reservoirs with a loss coefficient of 0.5 for the pipe entrance and a
loss coefficient of 1.0 for the pipe exit. The pipe is 2000 feet long with a roughness e of
0.002 inches. The kinematic viscosity of the water is 1.2x10-5 ft2/s. With a guess of f =
0.01466 find the flow Q. Was the guess of .01466 good? Show how to check your guess
using Haaland’s equation for the friction factor.
#5. Given an upstream reservoir that has its water surface elevation at 80 feet. A
downstream reservoir has its water surface at an elevation of H feet. A 12” diameter pipe
connects the two reservoirs with a loss coefficient of 0.5 for the pipe entrance and a loss
coefficient of 1.0 for the pipe exit. The pipe is 2000 feet long with a roughness e of 0.002
inches. The viscosity of the water is 1.2x10-5 ft2/s. The discharge in the pipe is 7.177 cfs
and there is a pump in the pipe that provides 150 horsepower of hydraulic power to the
flow. Find the elevation H using the Swamee-Jain equation to calculate the friction
factor.