QUESTIONS

1. What is a chute?

A chute is a canal of very steep slope.

2. What is an aqueduct?

An aqueduct is a canal to transport water for a specific use, typically over terrain, or elevated over a valley, stream or road.

3. What is a culvert?

A culvert is a covered conduit (or conduits) of relatively short length, usually flowing partially full, to enable a stream to cross a highway or other embankment.

4. What is potamology?

Potamology is the scientific study of rivers.

5. What is sinuosity in connection with rivers?

Sinuosity is the ratio of stream length to valley length.

6. What is a hydraulically wide channel?

A channel is hydraulically wide when the wetted perimeter P can be approximated by the top width T.

7. What ratio of top width to hydraulic depth can be considered hydraulically wide?

A channel may be considered hydraulically wide if the top width T is greater than or equal to 10 times the hydraulic depth D.

8. What is the typical range of the exponent β for trapezoidal channels?

Typical values of β for trapezoidal channels lie approximately in the range 1.35 ≤ β ≤ 1.65.

9. What is the most common type of current meter in the United States?

The most common type of cup meter is the Price current meter, which has six cups mounted on a vertical axis.

10. Why is the true velocity head greater than the velocity head computed based on mean velocity?

Due to the nonuniform velocity distribution over a cross section, the true velocity head is greater than the velocity head computed based on the mean velocity.

11. How does energy differ from momentum?

Energy is the integral of a force over a distance; momentum is the integral of the force over time. Energy is steady; momentum is unsteady.

12. How does the pressure distribution in the vertical vary under parallel flow?

Under parallel flow, the pressure distribution is essentially hydrostatic, with the pressure varying as a linear function of partial flow depth.

13. How does the pressure distribution in the vertical vary under convex curvilinear flow?

Under convex curvilinear, the pressure distribution is nonhydrostatic, with the pressure along the flow depth varying as a nonlinear function of partial flow depth. A piezometer located at the partial depth below the water surface would rise to an elevation which is lower than the water surface elevation.

14. How does the pressure distribution in the vertical vary under concave curvilinear flow?

Under convex curvilinear, the pressure distribution is nonhydrostatic, with the pressure along the flow depth varying as a nonlinear function of partial flow depth. A piezometer located at the partial depth below the water surface would rise to an elevation which is higher than the water surface elevation.

15. What is a channel of large slope?

A channel with slope greater than 10% is referred to as a channel of large slope. For a slope greater than 10%, the error in taking the vertical depth y in lieu of the pressure rise h is more than 1%.

PROBLEMS

1. What is the discharge per unit of width if the discharge is 24 m3/s and the channel top width is T = 8 m?

q = Q / T = 24 / 8 = 3 m2/s

2. Given: α = 0.4; β = 1.55; A = 45.6 m2. What is the discharge Q?

Q = α Aβ = 0.4 (45.6)1.55 = 149.09 m3/s

3. Given culvert diameter do = 1 m; what is the flow area for θ = 300°? (See Table 2-1).

A = (θ - sin θ ) (do2 / 8) = { [(5/6) 2 π ] - sin 300°} (12/8) = 0.7627 m2

4. What is the force F developed by a discharge Q = 10 ft3/s at a velocity V = 1 ft/s, at a cross section with a Boussinesq coefficient β = 1.05?

F = β ρ Q V = β (γ / g) Q V = (1.05) (62.4 lb/ft3 / 32.17 ft/s2 ) (10 ft3/s) (1 ft/s) = 20.367 lbs.

5. A stream of flow area A = 100 m2 is divided into three sections: (1) left overbank, with 20% of the flow area, and velocity 0.2 m/s; (2) inbank center, with 70% of the flow area, and velocity 1 m/s; and (3) right overbank, with 10% of the flow area, and velocity 0.1 m/s. Calculate the Coriolis coefficient α and the Boussinesq coefficient β.

 Segment ΔA V V 2 V 3 V ΔA V 2 ΔA V 3 ΔA Left overbank 20 0.2 0.04 0.008 4.0 0.8 0.16 Inbank center 70 1.0 1.00 1.000 70.0 70.0 70.0 Right overbank 10 0.1 0.01 0.001 1.0 0.1 0.01 Total 100 0.75 - - 75.0 70.90 70.17

V = ∑ V ΔA / ∑ ΔA = 75.0 / 100 = 0.75 m/s

α = ∑ V 3 ΔA / (V 3 A) = 70.17 / [(0.75)3 × 100] = 1.66

β = ∑ V 2 ΔA / (V 2 A) = 70.90 / [(0.75)2 × 100] = 1.26

6. Calculate the velocity distribution coefficients for the following canal data, with flow area A = 2768 ft2.

 Increment Velocity v(ft/s) Incrementalflow area ΔA (%) 1 3.5 0.5 2 4.0 2.9 3 4.5 10.3 4 5.0 23.5 5 5.5 52.7 6 6.0 10.1

Compare the results with those of approximate logarithmic formulas.

 Increment Velocity v (ft/s) Incrementalflow area ΔA (%) Incrementalflow area ΔA (ft2) v ΔA v2 ΔA v3 ΔA 1 3.5 0.5 13.840 48.440 169.54 593.39 2 4.0 2.9 80.272 321.088 1284.352 5137.408 3 4.5 10.3 285.104 1282.968 5773.356 25980.102 4 5.0 23.5 650.480 3254.4 16262 81310 5 5.5 52.7 1458.736 8023.048 44126.764 242697.202 6 6.0 10.1 279.568 1677.408 10064.448 60386.688 Sum 5.277 100.0 2768.000 14607.352 77680.46 416104.79

vm = ∑ vΔA / ∑ ΔA = 14607.352 / 2768 = 5.277

α = ∑ v3ΔA / (vm3 A) = 416104.79 / [(5.277)3 (2768)] = 1.023  ANSWER.

β = ∑ v2ΔA / (vm2 A) = 77680.46 / [(5.277)2 (2768)] = 1.0078  ANSWER.

ε = (vmax/vm) - 1 = (6.0/5.277) - 1 = 0.137

By formulas:

α = 1 + 3ε2 - 2ε3 = 1.051  ANSWER.

β = 1 + ε2 = 1.019  ANSWER.

7. A spillway is designed for a discharge q = 5 m2/s with a flow depth d = 0.5 m. What is the minimum radius of curvature of the spillway cross section to ensure that the pressure does not fall below 50% of hydrostatic?

V = q / d = 5 / 0.5 = 10 m/s

The pressure drop c = (d V 2) / (gr )

c /d = V 2 / (gr ) ≤ 0.5

r ≥ 2 V 2 / (g ) = 2 × 102 / (9.806) = 20.39 m

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140831 08:15