Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 13, Problem 140P
To determine
The manning coefficient of the channel.
The Froude number.
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QUESTION 4
Water flows in a rectangular channel at a depth of y₁ = 0.2 m and a flow rate of
7.5 m³/s. A hydraulic jump is generated and the width of the channel is 4 m. Chezy's
roughness constant for the channel is 56 SI units. Determine:
4.1 the depth downstream
4.2 the Froude number downstream
4.3 the head loss in the jump
4.4 the bed slope
Water flows through an open channel of hydraulic diameter 2.30 m, whose wetted perimeter is 7.00 m.
The slope is 0.0130, and the Chézy coefficient is 5.00 m0.5 s-1.
(a) Calculate the hydraulic radius. Give your answer in m, to 3 significant figures. (2 mark)
Hydraulic radius:
(b) Calculate the velocity of the water flow. Give your answer in ms1, to 3 significant figures. (4 marks)
Flow velocity:
m s-1
(c) Calculate the rate of discharge of the flowing water. Give your answer in cubic metres per second
(m³ s-1), to 3 significant figures. (4 marks)
Rate of discharge:
m3 s-1
Determine the most effi cient dimensions for a clay tilerectangular channel to carry 110,000 gal/min on a slopeof 0.002.
Chapter 13 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 13 - What is normal depth? Explain how it is...Ch. 13 - Prob. 2CPCh. 13 - Prob. 3CPCh. 13 - Prob. 4CPCh. 13 - What is the driving force for flow in an open...Ch. 13 - How does uniform flow differ from nonuniform flow...Ch. 13 - Prob. 7CPCh. 13 - Prob. 8CPCh. 13 - Prob. 9CPCh. 13 - Prob. 10CP
Ch. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15EPCh. 13 - Prob. 16PCh. 13 - Water at 10°C flows in a 3-rn-diameter circular...Ch. 13 - Prob. 18PCh. 13 - Water at 20°C flows in a partially full...Ch. 13 - Prob. 20CPCh. 13 - Prob. 21CPCh. 13 - Prob. 22CPCh. 13 - Prob. 23CPCh. 13 - Prob. 24CPCh. 13 - Prob. 25CPCh. 13 - Prob. 26CPCh. 13 - Consider steady supercritical flow of water...Ch. 13 - During steady and uniform flow through an open...Ch. 13 - How is the friction slope defined? Under what...Ch. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - Prob. 32EPCh. 13 - Prob. 33EPCh. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40CPCh. 13 - Prob. 41CPCh. 13 - Which is the best hydraulic cross section for an...Ch. 13 - Prob. 43CPCh. 13 - Prob. 44CPCh. 13 - Prob. 45CPCh. 13 - Prob. 46CPCh. 13 - Prob. 47PCh. 13 - Water flows uniformly half-full in a 2-m-diameter...Ch. 13 - Prob. 49PCh. 13 - A 3-ft-diameter semicircular channel made of...Ch. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Prob. 55PCh. 13 - Prob. 56PCh. 13 - Water is to be transported n a cast iron...Ch. 13 - Prob. 58PCh. 13 - Prob. 59PCh. 13 - Prob. 60PCh. 13 - Prob. 61PCh. 13 - Prob. 62PCh. 13 - Prob. 64EPCh. 13 - Prob. 65EPCh. 13 - Prob. 66PCh. 13 - Repeat Prob. 13-60 for a weedy excavated earth...Ch. 13 - How does gradually varied flow (GVF) differ from...Ch. 13 - How does nonuniform or varied flow differ from...Ch. 13 - Prob. 70CPCh. 13 - Consider steady flow of water; an upward-sloped...Ch. 13 - Is it possible for subcritical flow to undergo a...Ch. 13 - Why is the hydraulic jump sometimes used to...Ch. 13 - Consider steady flow of water in a horizontal...Ch. 13 - Consider steady flow of water in a downward-sloped...Ch. 13 - Prob. 76CPCh. 13 - Prob. 77CPCh. 13 - Water is flowing in a 90° V-shaped cast iron...Ch. 13 - Prob. 79PCh. 13 - Consider the flow of water through a l2-ft-wde...Ch. 13 - Prob. 81PCh. 13 - Water discharging into a 9-m-wide rectangular...Ch. 13 - Prob. 83PCh. 13 - Prob. 84PCh. 13 - Prob. 85EPCh. 13 - Water flowing in a wide horizontal channel at a...Ch. 13 - During a hydraulic jump in a W'ide chanrel. the...Ch. 13 - Prob. 93CPCh. 13 - Prob. 96CPCh. 13 - Prob. 97CPCh. 13 - Prob. 98CPCh. 13 - Prob. 99PCh. 13 - Prob. 100PCh. 13 - Prob. 101CPCh. 13 - Consider uniform water flow in a wide rectangular...Ch. 13 - Consider the uniform flow of water in a wide...Ch. 13 - Prob. 105PCh. 13 - Prob. 106EPCh. 13 - Prob. 107PCh. 13 - Prob. 108PCh. 13 - Water flows over a 2-m-high sharp-crested...Ch. 13 - Prob. 110EPCh. 13 - Prob. 111EPCh. 13 - Prob. 112PCh. 13 - Prob. 114PCh. 13 - Repeat Prob. 13-111 for an upstream flow depth of...Ch. 13 - Prob. 116PCh. 13 - Prob. 117PCh. 13 - Repeat Prob. 13-114 for an upstream flow depth of...Ch. 13 - Consider uniform water flow in a wide channel made...Ch. 13 - Prob. 120PCh. 13 - Prob. 121PCh. 13 - Water flows in a canal at an average velocity of 4...Ch. 13 - Prob. 123PCh. 13 - A trapczoda1 channel with brick lining has a...Ch. 13 - Prob. 127PCh. 13 - A rectangular channel with a bottom width of 7 m...Ch. 13 - Prob. 129PCh. 13 - Prob. 131PCh. 13 - Prob. 132PCh. 13 - Consider o identical channels, one rectangular of...Ch. 13 - Prob. 134PCh. 13 - The flow rate of water in a 6-m-ide rectangular...Ch. 13 - Prob. 136EPCh. 13 - Prob. 137EPCh. 13 - Consider two identical 15-ft-wide rectangular...Ch. 13 - Prob. 140PCh. 13 - Prob. 141PCh. 13 - A sluice gate with free outflow is used to control...Ch. 13 - Prob. 143PCh. 13 - Prob. 144PCh. 13 - Repeat Prob. 13-142 for a velocity of 3.2 ms after...Ch. 13 - Water is discharged from a 5-rn-deep lake into a...Ch. 13 - Prob. 147PCh. 13 - Prob. 148PCh. 13 - Prob. 149PCh. 13 - Prob. 150PCh. 13 - Prob. 151PCh. 13 - Prob. 152PCh. 13 - Prob. 153PCh. 13 - Water f1ows in a rectangular open channel of width...Ch. 13 - Prob. 155PCh. 13 - Prob. 156PCh. 13 - Prob. 157PCh. 13 - Prob. 158PCh. 13 - Prob. 159PCh. 13 - Prob. 160PCh. 13 - Prob. 161PCh. 13 - Prob. 162PCh. 13 - Prob. 163PCh. 13 - Prob. 164PCh. 13 - Prob. 165PCh. 13 - Prob. 166PCh. 13 - Consider water flow in the range of 10 to 15 m3/s...
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- Consider uniform flow through an open channel lined with bricks with a Manning coefficient of n = 0.015. If the Manning coefficient doubles (n = 0.030) as a result of some algae growth on surfaces while the flow cross section remains constant, the flow rate will (a) double, (b) decrease by a factor of √2, (c) remain unchanged, (d) decrease by half, or (e) decrease by a factor of 21/3.arrow_forwardAn irrigation channel is to carry a discharge of 14 cumec with a velocity of 0.9 m/s and bed slope of 1 in 2500. The side slopes are 1 to 1. Find the depth and bottom width. The values of Chezy" C for this channel for different values of hydraulic radius R are as tabulated below. Hydraulic radius R 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Chezy's C 34 35 37 38 39 40 41 41arrow_forwardWater flows uniformly in a rectangular channel with finished-concrete surfaces. The channel width is 3 m, the flow depth is 1.2 m, and the bottom slope is 0.002. Determine if the channel should be classified as mild, critical, or steep for this flow.arrow_forward
- The water flows in the channel with a base slope of 0.003 and the cross-section shown in Figure 3. The dimensions of different subdivisions and the Manning coefficients for surfaces are also shown in the figure.a) calculate the volume flow flowing through the Channel.B) calculate the Manning coefficient.arrow_forwardA trapezoidal channel having a bottom slope of 0.001 is carrying a flow of 30 m/s. The bottom width is 10.0 m and the side slopes are 2H to 1V. A control structure is built at the downstream end which raises the water depth at the downstream end to 5.0 m. Compute the water surface profile till 1.20 m. Manning n is 0.013 and a = 1. Select an appropriate Month for your calculations. Please read the question carefully and provide the correct solution with simple steps fast. Please answer quickly.arrow_forwardA sharp-crested triangular weir with a notch angle of 80° is used to measure the discharge rate of water from a large lake into a spillway. If a weir with half the notch angle (? = 40°) is used instead, determine the percent reduction in the flow rate. Assume the water depth in the lake and the weir discharge coefficient remain unchanged.arrow_forward
- Given: Asked: Solution:arrow_forwardIn flowing from section (1) to section (2) along a rectangular open channel, the water depth decreases by a factor of three and the Froude number changes from a subcritical value of 0.7 to a supercritical value of 3.4. Determine the channel width at (2) if it is 8 ft. wide at section (1). Assume stead-state flow.arrow_forwardA small stream has a trapezoidal cross- section with base width of 12 m and side slope 2 horizontal: 1 vertical in a reach 8 km. During the high water levels record at the ends of the reach are as follows Section elevation of bed (m) water surface elevation (m) remarks Upstream 100.20 102.70 Manning's n=0.030 Downstream 98.60 101.30 Estimate the discharge in the stream.arrow_forward
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