### CEE 332 Hydraulic Engineering: Practice Prelim 2 solutionApril 18, 2003 - 2:30-4:30 PMClosed book, two 8.5” x 11” summary sheets

Note: The last page of this exam is an equation sheet!

Read each problem carefully before beginning to work on the answer!

Make sure you answer each part of each question. May the time you spent preparing for this exam pay off.

#### Short Answer or Quick Calculation

1) Explain the difference between lumped and distributed approaches for transient analysis.

In lumped all of the water in a pipe has the same velocity at any instant in time. In a distributed approach the velocity is a function of both time and location.

2) In the transient laboratory exercise the pressure gradually increased behind the solenoid valve after the valve closed. Explain how you could have used the ideal gas law to calculate the pressure as a function of time.

Pressure is a function of the moles and volume of gas. The decrease in the volume of gas is equal to the cumulative flow of water since the valve closed.

3) Under what conditions are the energy and hydraulic grade lines parallel in open channel flow?

When the velocity isn’t changing with location (uniform flow).

4) Name three equations that could be used to calculate the slope of the energy grade line in open channel flow.

Darcy Weisbach, Manning, Chezy.

5) Does specific energy increase or decrease if the flow is supercritical and the water depth is increasing?

decrease

#### Problem solving (64 points). Note that there are constants and equations on the last sheet of the exam

1) (9 points) A small pebble was dropped into a wide channel and the velocity of the spreading ripples was measured. The ripples that were going downstream the fastest were traveling at 3 m/s and the ripples that were going downstream the slowest were traveling at 1 m/s.

a) (3 points) What was the depth of the channel?

c=1m/s, V=2 m/s y=0.1 m

b) (3 points) What was the specific flow rate?

q=yV = 0.2 m2/s

c) (3 points) What was the Froude number?

Fr=V/c=2

2 (30 points) A 5 m wide rectangular channel with bottom slope of 0.001 and Manning n of 0.02 has a sluice gate at the upstream end that lets water enter the channel from a reservoir. The sluice gate is opened 10 cm (measured from the channel bottom) and the depth of water behind the sluice gate is 2 m (measured from the channel bottom). for a sluice gate and the discharge coefficient for this sluice gage is 0.6.

A) (3 points) Calculate the flow rate into the channel.

1.88 m3/s

B) (5 points) Estimate the water depth just downstream of the sluice gate assuming specific energy is conserved (note that you may neglect the velocity head in the reservoir) and using the flow rate that you calculated in A (HINT: to avoid iteration use the fact that most of the energy is in one form to simplify the energy equation).

y=0.06 m

C) (3 points) Why is the depth of water immediately downstream from the sluice gate less than 10 cm?

vena contracta

D) (5 points) Calculate normal depth for this channel for a flow of 2 m3/s. (you may approximate by assuming the channel is wide and hence the hydraulic radius is equal to the depth).

yn=0.44 m

E) (4 points) Calculate critical depth for a flow of 2 m3/s.

yc=0.25 m

F) (5 points) Sketch and label (M1, etc.) the downstream surface profile for a flow of 2 m3/s assuming the channel is very long and the downstream boundary condition is critical depth. Include lines for the normal and critical depths.

M3, hydraulic jump, M2

G) (5 points) Use the direct step method to calculate the distance for the water level to increase from a depth of 10 cm to a depth of 12 cm using a single step for a flow of 2 m3/s. You may use the average depth to estimate the friction slope.

Distance is 2.3 m

3 (25 points) The penstock feeding the Cornell University Hydroplant on Fall Creek is 550 m long, 1.5 m in diameter, and carries a design flow of 5 m3/s. The elevation difference between Beebe lake and the turbines is 36 m. The penstock is made of 2.5 cm steel pipe with a bulk modulus of elasticity of 200 GPa. The friction factor for the pipe is approximately 0.02 and the sum of the minor loss coefficients is 5. The bulk modulus of elasticity for water (K) is 2.2 GPa.

A) (5 points) If the valve at the turbine were opened instantaneously, how long would it take for the water in the penstock to accelerate from zero to the design flow?

t=4.54 s

B) (5 points) Calculate the pressure rise (in kPa) in the pipeline for an instantaneous valve closure at the turbines.

3.26 MPa

C) (5 points) How long would it take for the pressure wave to make one complete cycle?

t=1.9 s

D) (5 points) If a valve at the turbines is closed so the flow rate is ramped to zero at a constant deceleration over 20 seconds what will the total pressure be at the valve (in kPa) the instant before the flow stops?

static pressure is 353 kPa

Pressure to cause deceleration is 77.8 kPa (from F=ma)

Total pressure is 430 kPa

E) (5 points) Why is a lumped system approach appropriate for D?

t>4L/a

3

#### Physical constants (for water at 20°C)

density = 1000 Kg/m3

specific weight = 9789 N/m3

viscosity = 1 x 10-3 N·s/m2

kinematic viscosity = 1 x 10-6 m2/s

vapor pressure = 2340 Pa

atmospheric pressure = 100 kPa

bulk modulus of elasticity (K) = 2.2 GPa

#### General Equations

, or

laminar flow

(Swamee Jain)

(expansion)

(minor losses)

#### Cavitation in pumps

#### Open Channel Flow

(SI units)

in general

sluice gate

Hyperbolic tangent

3