Hydraulic Engineering Second Exam Spring 2012(115/100) Full Name: ______KEY_______

Rules: one page cheat sheet one sided allowed; Walton text notes and textbook. No: cell phones, non-FE 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 but otherwise count the same.

  • 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.A passive rainwater harvesting system is to be installed in conjunction with a parking lot. The system consists of a set of shallow depressions in a 10 foot wide swath in the middle of a 200 by 200 foot parking lot. The depressions are two feet deep and backfilled with size sorted gravel having a final porosity of 35%. The parking lot halves each slope into the depressions. For really large storms, the depressions will overflow into a storm sewer. For small storms the depressions will capture and infiltrate all the water. The soil below and surrounding the depressions has a field capacity of 0.3 and a permanent wilting point water content of 0.15. The depression is planted with Honey Mesquite trees that, when fully grown, will have a crown with a 30 foot width (i.e, will cover the depressions and extend 10 ft. out into the parking lot on each side). The Mesquite trees have a transpiration rate of 0.04 inch/day over the crown area. The Rational Coefficient for the parking lot is 0.90.

Table 1-2. El Paso Rainfall Amounts (inches per storm)
Return Period
Duration / 1 yr / 2 yr / 5 yr / 10 yr / 25 yr / 50 yr / 100 yr
30 min / 0.6 / 0.7 / 1.0 / 1.2 / 1.4 / 1.6 / 1.8
1 hr / 0.7 / 0.9 / 1.3 / 1.4 / 1.7 / 1.9 / 2.2
2 hr / 0.8 / 1.0 / 1.4 / 1.7 / 2.0 / 2.2 / 2.5
3 hr / 0.8 / 1.1 / 1.5 / 2.0 / 2.1 / 2.5 / 2.8
6 hr / 1.0 / 1.5 / 2.0 / 2.1 / 2.8 / 3.0 / 3.5
12 hr / 1.1 / 1.5 / 2.2 / 2.5 / 3.0 / 3.5 / 3.8
24 hr / 1.2 / 1.6 / 2.4 / 2.9 / 3.4 / 3.7 / 4.0

a)(5) What volume of water can be held in the depressions in cubic feet?
2 ft x 10 ft x 200 ft *0.35 = 1400 cubic feet

Note: give two points if they do it right except for porosity

b)(10 for Q+10 for volume) What fraction of the 24-hour 100 year storm will be stored in the depressions and how much will overflow into the storm sewer?
Q=CIA Vol=CIA*time but I*time = depth = 4 inches = 1/3 foot

Vol= 0.9 * 40000 /3 = 12,000 cubic feet

Depression fraction = 1400/12000 = 0.117 storm sewer fraction = (12000-1400)/12000 = 0.883
Note: don’t penalize them for getting part a wrong

c)(10) How much water will be used every day by the trees during the growing season (May – October) in cubic feet/day?

2.(10) If a passive rainwater harvesting system is designed for the 10 year drought (5 inches/year precipitation) to be survived without watering; what is the probability that the system will require extra watering one or more times in the next 15 years?
P=1-(1-p)^n = 1-(1-0.1)^15 = 0.794

3.(20) The runoff above on Jesse Creek came from a single rainstorm that started at time = 0 and lasted for one hour. The drainage basin is 96 hectares. Use it to make a unit (1 cm) hydrograph. Draw the unit hydrograph on the figure.
volume = 4 m^3/s*hour*3600 s/hr = 14,400 cubic meters

Depth = volume/area = 14400/(39.2*10^4)= 0.015 m = 1.5 cm

Scale factor = 1/1.5 = 2/3 = 0.6667

New peak = 2*2/3 = 4/3 = 1.33 m^3/s
answer: unit hydrograph starts at t=1, Q=0 then diagonal to (t=3, Q=1.33), then flat to (t=4, Q=1.33), then diagonals down to (t=5 hr, Q=0)
Extra copy of graph (in case you redo your answer)

4.(10) The markings are every 10 cm, the tube is 1 m long, the piezometers show the water level. The hydraulic conductivity is 10-4 cm/s. Find the rate and direction of flow in the tube. Datum is the bottom of the figure. Show total head, pressure head, and elevation head at each piezometer location.

Point 1: z=40 cm, p/rho g = 110 cm, h = 150 cm

Point 2: z=80 cm, p/rho g = 50 cm, h = 130 cm

V=-K(h2-h1)/100 cm =- 10^-4 cm/s*(120-150)/100 =+2*10^-3 cm/s

5.(5) What is the initial abstraction for a soil with a curve number of 35 using the SCS method?
answer: about 4.6 inches, read it directly from graph, (note: graph is actually plotted incorrectly & that is why it doesn’t match the equations)


6.(5) Hydraulic head has units of: a) m2, b) J/N, c) W, d) N

7.(10) Draw the watershed for Jared Branch where it enters the Rose River.


8.(15) Label the three lines on the Probability Density Function (PDF) as: mean, median, or mode

Left:mode, middle median, right average

Some Equations that May Be Useful

The Binomial distribution is:

(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