Hydraulic Engineering Final Exam Fall 2012
KEY (112/100)
Full Name: ___________________________________________
Rules: two page cheat sheet one sided allowed; Walton text notes and textbook. No: cell phones, non-ABET calculators, or other
materials. Fill in the answers in the space provided with units; use the white space to show your work. You MUST show work to
receive credit & all answers MUST have appropriate units. Extra credit problems are more difficult.



Casio: All fx-115 models. Any Casio calculator must contain fx-115 in its model name.
Hewlett-Packard: The HP33s and HP 35s models, but no others
Texas Instruments: All TI-30X and TI-36X models. Any Texas Instruments calculator must contain either TI-30X or TI-36X
in its model name.
I promise that I did not use any unauthorized material or was helped by anyone or helped anyone in this exam.
SIGNATURE:____________________________________
1.
(24) Note that one horse power equals 550 foot pounds/second; the kinematic viscosity is 1.4 *10 -5 foot2/s; the roughness height is
0.00015 ft; both tanks are 100 ft deep and have a diameter of 14 ft.
4 points for each part, no difference between test versions (changed numbers make no difference)
a)
The Reynolds number is:
1.82*105
b) The friction factor is:
0.0265 from Moody Diagram (allow 0.026 to 0.027
c)
Solving the energy equation for the required pumping head gives:
hpump=Z+hloss = 100 ft + V2/2g(f L/D)
d) The required pumping head is:
185.6 ft (note give them credit if this is answer to e) + 100 ft)
e)
The head loss from friction is:
85.6
f)
The required horsepower is:
30 hp
If they got A or Reynolds number wrong I punished them once and counted the rest right
Note error in friction factor in copied answer:
2. (12) The solid lines are labeled; the dashed line is the system curve. If the pump rpm (revolutions per minute), is
3850, how much water do we pump and what is the power input ? Show your work by drawing on the figure. What is
the efficiency?
Note: dashed line location changes between test versions
Q=125 L/s, hp=100, Efficiency about 56%, grade on their arrows
I deducted half of the credit if they used wrong curve but followed the right method
3.
(20) After a 1.2 inch precipitation event lasting for 30 minutes the water is flowing at a depth of 1.49 feet in the triangular
channel shown with slope of 0.002, n of 0.018., and tea colored water.
Note: test versions differ on n=0.012 or 0.018
a)
The hydraulic radius is:
0.527
b) The flow velocity is:
2.41 ft/s or 3.62 m/s
c)
The discharge is:
5.36 or 8.04 cfs
d) The Froude number is:
0.49 or 0.74
e)
The channel is:
MILD
If they got A or P wrong I punished them once and counted the rest right
4. (12) The sand filter shown in figure 7.7.1 is 1 m deep and has a surface area of 2 m2. If the permeability is 0.55 cm/s,
determine the discharge through the filter.
Versions differ on area.
Discharge is 0.0088 or 0.0132 cubic meters per second
No partial credit except I gave half credit if the velocity is correct
V= .44 cm/sec for both versions.
A lot of students missed this question
5. (20) Which pipe has a greater diameter? Or are they the same? What is the (approximate) velocity of the water at
location T? Where is the pressure greatest in the system? Where is the pressure the lowest in the system? Units in feet, at
least one of the answers may require a graphical estimate based upon the figure.
How does changing datum change the location of the EGL and HGL?
Versions are the same:
Last pipe has greatest diameter
Assuming distance between EGL and HG at location T is 40 ft (allow great leeway here)
V2/2g = 45 ft or V = sqrt(45 ft *2*32.2) = 50.7 ft/s
I allowed EGL-HGL from 25 -50 ft. no partial credits.
6. (16) A river has a mean peak annual flow rate of 300 cfs with a standard deviation of 45 cfs. We need to find the 25 year
flood in order to design an irrigation structure. (10 points)
Versions differ on 300 or 200 cfs mean
Find the 25 year flood discharge:
379 or 278 cfs, the main thing is: flood discharge = mean + sigma*z where z = about 1.75
I deducted 5 points if z value is wrong but the rest of calculations are correct
What is the probability that the 50 year flood will be exceeded exactly twice in the next 30 years? (6points)
Versions differ on 25 yr versus 50 year flood
7. (8) A 100 acre parking lot with a C of 0.9 is subjected to a 0.02/yr probability storm. The time of concentration is 15
minutes, the Manning n is 0.013 and the slope is 0.5%. Estimate the discharge in cfs.
Versions differ in 50 year versus 5 year storm, note that units almost work out without any conversion, it is OK if they use
that, my chart reads are crude
For version a
I= 5 in/hr not
4.5 and I
allowed
between 4.9 –
5.1.
You have right
for version b =
3.8 I allowed
between 3.73.9>
I gave zero if
they use
wrong
probability
because it
means they
cheated.
Some Equations that May Be Useful
The Binomial distribution is:
x
n – x 
n!
P x  = -----------------------p  1 – p 
x!  n – x !
(2)
where
P(x)
=
probability of obtaining x successes in n trials (e.g., getting 3 heads in 10 coin tosses)
p
=
probability of getting a success in each trial (e.g., the probability of getting a head in a coin toss is 0.5; the probability of
getting a 25 year storm in any one year is 0.04)
n
=
number of trials (e.g., number of coin tosses or number of years in the design life of the subdivision)
x
=
number of successes (e.g., number of heads; number of floods)
The normal distribution Z = (x-µ)/σ