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 116P
To determine
The percent reduction in the flow rate.
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Question
: A stream bed has a rectangular cross section 5 meters wide and a slope of
0.0002 m/m. The flow rate in the stream is 8.75 m³/s. A dam is built across the stream, causing
the water surface to rise to 2.5 meters just upstream of the dam, as shown below. Assume n =
0.015.
y = yn
2.5 m
a. Find the normal depth, yn, corresponding to this flow rate and channel geometry. You do
not need to solve the equation by hand. To get full credit, show your equation with only
one unknown.
b. Find the critical depth, yc.
c. The yn is found to be 1.8 m by solving the equation numerically. Identify the water
surface profile upstream of the dam. Explain your answer for full credit.
3.In one section of the irrigation canal, the narrowing of 1.5 times the width upstream (as
shown in the figure below). If the uniform channel cross section is rectangular with the
downstream width (b2) = 4.5 m, the velocity (V1) and depth (y1) of the upstream flow are
measured to be 0.2 m/s and 4.0 m, determine the energy loss (hf ) due to channel narrowing
if the downstream flow depth is assumed to be the same as the upstream flow depth !
b2
bị
V1
2.Water flows through a rectangular channel with a width b = 2 m and a height (Pw) = 1 m, the flow rate ranges from Qmin = 0.02 m^3/s and Qmax = 0.60 m^3/s. This flow rate is measured using
Rectangular sharp-crested weir
Triangular sharp-crested with = 90^o
Broad-crested weir
Plot onto the graph Q = Q(H) for each type of weir and give your analysis which type of weir is most appropriate to apply
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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- A stream bed has a rectangular cross section 5 meters wide and a slope of 0.0002 m/m. The flow rate in the stream is 8.75 m³/s. A dam is built across the stream, causing the water surface to rise to 2.5 meters just upstream of the dam, as shown below. Assume n = 0.015. y≈yn 2.5 m 1. Find the normal depth, yn, corresponding to this flow rate and channel geometry. You do not need to solve the equation by hand. To get full credit, show your equation with only one unknown. (10 pts) 2. Find the critical depth, yc. (10 pts) 3. The yn is found to be 1.8 m by solving the equation numerically. Identify the water surface profile upstream of the dam. Explain your answer for full credit. (10 pts)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_forward4. Find the width, in meters, of the channel at the back of a suppressed weir using the following data: H= 28.5cm d= 2.485m Q = 0.84m/s Consider velocity of approach.arrow_forward
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