# 978-0134292380 Chapter 6 Part 1

Document Type

Test Prep

Book Title

Fundamentals of Hydraulic Engineering Systems 5th Edition

Authors

A. Osman H. Akan, Ned H. C. Hwang, Robert J. Houghtalen

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TEST QUESTIONS & PROBLEMS - CHAPTER #6

Short Answer Questions

1. The flow of water in a small stream during a rainfall event can be described as:

a) steady and uniform b) steady and rapidly varied c) steady and gradually varied

d) unsteady and uniform e) unsteady and rapidly varied f) unsteady and gradually varied

2. What is the difference between steady and uniform flow?

3. (T or F) In gradually varied flow, the channel bottom, water surface, and EGL are parallel.

4. What is the difference between normal depth and uniform depth?

5. The flow of water in a prismatic irrigation canal during dry weather can be described as:

a) steady and uniform b) steady and rapidly varied c) steady and gradually varied

e) unsteady and uniform e) unsteady and rapidly varied f) unsteady and gradually varied

6. (T or F) Manning’s equation is derived from an energy balance.

7. What type of flow regime is appropriate for the application of Manning’s equation?

8. The derivation of Manning’s equation is based upon:

a) Newton’s 2nd Law b) impulse-momentum principles c) Bernoulli principle

d) continuity principle e) Darcy-Wesibach

9. Sketch a profile view of uniform open channel flow and label the channel bottom, the HGL,

and the EGL. Also identify the three major components of energy on the figure.

Ans. See Figure 6.1 in the textbook.

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10. What is the definition of wetted perimeter in open channel flow terminology?

11. What is the definition of hydraulic radius in open channel flow terminology?

12. What are the three forces that are considered in the force balance on a control volume that

leads to the development of Manning’s equation for uniform flow?

13. Which force term leads to the introduction of hydraulic radius in Manning’s equation?

a) hydrostatic pressure b) the weight of the water c) impulse-momentum

d) the resistance force exerted by the channel on the flow

14. Derive the relationship between depth of flow and width for a rectangular channel that is the

most hydraulically efficient (i.e., best hydraulic section). Show all steps.

15. If a semicircle represents the best hydraulic section, give two reasons why this shape isn’t

used for constructed water conveyance channels.

16. What is the width to depth relationship for the best rectangular hydraulic section?

17. (T or F) In constructed channels, the vertical distance from the designed water surface to the

top of the channel banks is known as the freeboard of the channel.

18. In the derivation of critical depth, the equation (Q2T)/(gA3) = 1 became V2/(gD) = 1. Show

the steps that led to the final equation and define T and D.

19. A Froude number of 0.8 indicates:

a) subcritical flow b) critical depth c) same as “e” d) normal depth e) there is no “e”

20. (T or F) Normal depth is the depth of flow when the specific energy is at a minimum.

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21. Starting with the specific energy equation for open channel flow, E = V2/2g + y, show that

you will arrive at (Q2T)/(gA3) = 1 for critical depth (i.e., for minimum energy). Show and

22. Which statement below is incorrect?

(a) In a given channel the flow depth is higher than the critical depth for the same discharge

when the flow is subcritical

(b) In a given channel the specific energy for a given discharge is always higher for

supercritical flow than for subcritical flow.

(c) The critical depth in a channel for a given discharge does not depend on the longitudinal

bottom slope of the channel

(d) None of the above

23. Draw a specific energy curve for a given flow rate, label axes, identify critical depth,

subcritical flow, and supercritical flow.

24. Which of the following statements is not true when describing the Froude number?

a) The Froude number is the ratio of the mean flow velocity to the speed of a surface wave.

b) The Froude number is derived from the specific energy equation.

c) The Froude number is used to determine normal depth.

d) If Nf < 1, flow is subcritical, and if Nf > 1, flow supercritical.

e) The concept of top width is introduced in the derivation of the Froude number.

25. Write out the equation for the Froude number. What is it a ratio of and what is it used for?

26. (T or F) The difference between energy and specific energy in open channel flow is that the

specific energy uses the channel bottom as a datum (reference).

27. Derive the equation for critical depth in a rectangular channel starting with the Froude

number and setting it equal to unity: Nf = V2/gy = 1.

yc

subcritical

supercritical

Specific energy, E

Depth, y

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28. A rectangular channel has a bottom width of 10 ft, longitudinal bottom slope of 0.0001, and a

Manning roughness factor of 0.016. If the critical depth in the channel is 1.91 ft

(a) The discharge in the channel is nearest 150 cfs

(b) The discharge in the channel is nearest 22 cfs

(c) The discharge in the channel is nearest 623 cfs

(d) Not enough information is given to determine the discharge.

29. Channels A and B have identical characteristics except A has a steeper longitudinal slope.

Determine which of the statements below is correct for the same discharge in both channels

(a) The critical depth in channel A is larger than the critical depth in channel B

(b) The critical depth in channel A is smaller than the critical depth in channel B

(c) The critical depth in channel A is same as the critical depth in channel B

(d) Critical flow does not occur in the steeper channel

30. The appropriate equations for analysis of a hydraulic jump are based on which underlying

concepts? a) energy principles b) momentum principles c) friction loss principles

d) uniform flow principles e) continuity principles

31. (T or F) Hydraulic jumps occur in open channels when the flow changes from subcritical to

supercritical.

32. What is the difference between alternate depth and sequent depth?

33. The depth of flow downstream of a hydraulic jump is known as

a) normal depth b) critical depth c) alternate depth d) sequent depth e) “a” and “d”

34. (T or F) The depth of flow prior to a hydraulic jump (initial depth) and the depth after the

jump (sequent depth) have the same specific energy.

35. The flow in a mild-sloped stream during a flood event can be described as

a) steady b) unsteady c) uniform d) rapidly varied e) gradually varied

36. What is the relationship between critical depth and normal depth in channels that are

classified as steep.

37. (T or F) In gradually varied flow, the channel bottom, HGL, and EGL are all parallel.

38. What type of gradually varied flow profile would you expect upstream of a dam that is

located on a mountain stream?

a) S-1 b) M-1 c) S-2 d) M-2 e) S-3 f) M-3

39. The figure to the left has a (M, C, or S) channel classification and a (1, 2, or 3) flow

classification. The figure to the right is a (M, C, or S) channel and a (1, 2, or 3) flow.

40. Which of the following descriptors are appropriate in describing the flow phenomenon of a

flood wave moving down the Mississippi River or the Nile River?

a) steady b) unsteady c) uniform d) rapidly varied e) gradually varied

41. A trapezoidal channel carrying 300 cfs has a bottom width of 12 ft, side slope of 2 and a

longitudinal bottom slope of 0.02. The critical depth is 2.34 ft and the normal depth is 1.25. If

the flow depth at a given section is 3.5 ft, the flow profile in the channel is of type

(a) M-2 (b) S-1 (c) S-2 (d) None of the above

42. What type of gradually varied flow profile do we have if yn < y < yc? If y > yn < yc?

43. (T or F) A control section in an open channel is a location where the relationship between

depth and discharge is known.

44. A rectangular channel carrying 200 cfs has a bottom width of 12 ft and a longitudinal bottom

slope of 0.001. It has a critical depth of 2.32 ft and a normal depth of 4.0. If the flow depth at

a given section is 3.5 ft determine which statement below is incorrect

(a) The flow profile is of type M-2 (b) The flow depth increases in the flow direction

(c) The depth decreases in the flow direction (d) The Froude number is less than one.

45. What is the principle upon which water surface profiles are determined?

46. Which principle is not used in the solution of water surface profile computations?

a) mass balance b) energy balance c) momentum balance d) Manning’s equation

47. A trapezoidal channel carrying 280 cfs has a bottom width of 12 ft, side slope of 2 and a

longitudinal bottom slope of 0.001. The critical depth is 2.25 ft and the normal depth is 2.78.

The flow depth at the downstream end of this channel is 3.12 ft. Determine which of the

statements below is correct

(a) A flow depth of 2.55 ft will not occur in this channel.

(b) The flow depth decreases in the flow direction.

(c) If the channel is very long, a hydraulic jump will occur.

(d) None of the above

48. A very long trapezoidal channel has a bottom width of 18 ft, side slope of 2, longitudinal

bottom slope of 0.01, Manning roughness factor of 0.020, and it carries 800 cfs. The normal

depth is 9.25 ft and the critical depth is 3.45 ft. The flow depth at a section along this channel

is 3.70 ft. The flow depth 10 ft upstream is most likely to be

(a) 3.79 ft (b) 3.61 ft (c) 5.20 ft (d) 3.45 ft

49. What must be true for a channel to be classified as a critical channel ?

Ans. yn = yc

50. What type of gradually varied flow profile is likely to occur when water flows from a

reservoir into a spillway?

a) S-1 b) M-1 c) S-2 d) M-2 e) S-3 f) M-3

51. (T or F) Open channels are generally designed for uniform flow conditions.

52. Give three examples of flexible channel liners.

53. Give three examples of rigid channel liners.

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Problems

1. A triangular roadside channel has side slopes of 3:1 (H:V) and a longitudinal slope of 0.01.

Determine the flow rate in the concrete channel if uniform flow is assumed when the top

width of the flowing water is 2 meters.

2. Water flows at a depth of 1.83 m in a trapezoidal, riprap lined channel with a bottom width of

3m, side slopes of 2:1 (H:V), and a bottom slope of 0.005. Determine the discharge in the

channel assuming uniform flow. Check your solution using Figure 6.4.

3. A discharge of 2,200 cfs flows in a trapezoidal channel at a normal depth of 8.0 ft. The

channel has a slope of 0.01, a 12 ft bottom width, and side slopes of 1:1 (H:V). Determine the

Manning coefficient of channel roughness. Also determine the sensitivity range of the

roughness coefficient estimate if the flow rate can only be estimated to within ±200 cfs?

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