- (20%) A 100-acre watershed has two distinct subareas: (1) an undeveloped portion, of 35 ac and runoff coefficient C= 0.3,
and (2) a developed portion, of 65 ac and C = 0.7. If the 10-yr rainfall intensity is 0.5 in/hr; what is the
peak flow by the rational method? Calculate the exact value (in cfs), using the appropriate unit conversions.
Qp = C I A = I Σi (CiAi) = 0.5 in/hr × [(0.3 × 35 ac) + (0.7 × 65 ac)]
Qp = 0.5 in/hr × 56 ac × [1/12 ft/in) / 3600 s/hr] × 43560 ft2/ac = 0.5 × 56 × 1.00833
Qp = 28.23 cfs.
- (20%) A rectangular channel is to be designed to convey 100 cfs. The bottom width is b = 10 ft,
the bottom slope is So = 0.001, and the Manning's n = 0.013. Calculate the design flow depth (3 significant digits)
using trial and error.
Manning equation:
Q = (1.486/n) A R2/3 S1/2
Q = (1.486/n) A5/3 S1/2 P-2/3
Try y = 1 ft.
Q = (1.486/0.013) 105/3 × 0.0011/2 12-2/3 = 32.01 cfs.
Try y = 2 ft.
Q = (1.486/0.013) 205/3 × 0.0011/2 14-2/3 = 91.70 cfs.
Try y = 2.1 ft.
Q = (1.486/0.013) 215/3 × 0.0011/2 14.2-2/3 = 98.53 cfs.
Try y = 2.12 ft.
Q = (1.486/0.013) 21.25/3 × 0.0011/2 14.24-2/3 = 99.91 cfs.
Try y = 2.13 ft.
Q = (1.486/0.013) 21.35/3 × 0.0011/2 14.26-2/3 = 100.6 cfs.
- (20%) A rectangular channel has a discharge q = 2 m3/s/m. What is the critical depth? What is the critical velocity?
yc = [q2/g]1/3
yc = [22/9.81]1/3
yc = 0.742 m
vc = q / yc = 2 / 0.742 = 2.697 m/s
- (20%) A broad-crested weir has a length L = 12 ft and design head H = 1.5 ft.
In the absence of any other information, what is the best estimate of the design discharge (in cfs)?
Q = CL H3/2 = 3.09 × 12 ft × 1.53/2
Q = 68.1 cfs.
- (20%) Please answer questions in a brief statement.
- What is the time of concentration? In the most general case (Papadakis formula), what four physical variables is it a function of? Which two variables are in the numerator? Which two are in the denominator?
The time of concentration is the time required for a drop of water to travel on the land surface,
from the most distant point in the watershed to the outlet.
In the Papadakis formula, the time of concentration varies as a function of length L, slope S, rainfall intensity i, and roughness factor n.
Time of concentration is directly proportional to L and n, and inversely proportional to i and S.
- What is the difference between the Manning and Chezy equations? State three differences.
- In the Chezy equation, hydraulic radius R is elevated to the 1/2 power.
In the Manning equation, R is to the 2/3 power.
-
The Chezy coefficient appears to be dimensional, but can be readily converted to dimensionless form.
On the other hand,
the Manning coefficient appears dimensionless, but it is not (a 1.486 unit conversion coefficient is applicable in U.S. Customary units).
-
The Chezy equation is theoretical; the Manning equation is practical.
-
The Chezy equation was developed in 1776; the Manning equation in 1889.
- What four forces are normally present in open-channel hydraulics? What two of these forces are present
in hydraulic jump analysis? Why?
Gravity, friction, pressure gradient, and inertia.
Only the pressure gradient and inertia are used to derive the hydraulic jump equation. Gravity is neglected because the hydraulic jump occurs in a horizontal
reach of channel. Friction is neglected because the lenght of the jump is relatively short to the rest of the channel.
- How does Froude's Law differ from the Froude number as currently used in hydraulic engineering practice?
Froude's law dealt with ship hydrodynamics:
V ∝ (L)1/2
which leads to:
V = k (L)1/2
where L is the ship (prototype or model) length, and k = a proportionality factor (dimensional).
The Froude number (dimensionless) is:
F = V / (gD)1/2
where D = hydraulic depth of the open-channel flow (D = A/T), and
g = gravitational acceleration.
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