Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 13, Problem 113P
To determine
The percent reduction in flow rate.
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7.5 m
-2.0 m
6.0 m
h
where b = weir width (m) 2
g = gravitational acceleration (m/s)
h = height of water above the weir edge (m)
2.0 m
1.0 m wide weir
water flows
out through
this opening
The surge tank pictured (shown with clear sides for illustration purposes)
is used to even out variable flows. During periods of high flow, excess
water is diverted to the surge tank where it flows out more slowly over
the weir. The volumetric flow over the weir is
V = 0.011 * b* g¹/2h³/2
Assuming no excess flow is currently being diverted to the surge tank,
determine the time required for the water level in the tank to become 6.25
m if the initial height is 7.5 m
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.
An irrigation channel of trapezoidal section, having side slopes 3
horizontal to 2 vertical, is to carry flow of 10 cumec on a longitudinal
slope of 1 in 5000. The channel is to be lined for which the value of
friction coefficient in Manning's formula is n = 0.012. Find the dimensions
of the most economic section of the channel.
Chapter 13 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 13 - What is the driving force for flow in an open...Ch. 13 - How does open-channel flow differ from internal...Ch. 13 - Prob. 3CPCh. 13 - Prob. 4CPCh. 13 - What is normal depth? Explain how it is...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. 11CPCh. 13 - Water at 20°C flows in a partially full...Ch. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - Water at 10°C flows in a 3-rn-diameter circular...Ch. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - Prob. 20CPCh. 13 - Prob. 21CPCh. 13 - Prob. 22CPCh. 13 - Prob. 23CPCh. 13 - Prob. 24CPCh. 13 - Prob. 25CPCh. 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. 29PCh. 13 - Prob. 30EPCh. 13 - Prob. 31EPCh. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38CPCh. 13 - Which is the best hydraulic cross section for an...Ch. 13 - Prob. 40CPCh. 13 - Prob. 41CPCh. 13 - Prob. 42CPCh. 13 - Prob. 43CPCh. 13 - Prob. 44CPCh. 13 - Prob. 45PCh. 13 - A 3-ft-diameter semicircular channel made of...Ch. 13 - A trapezoidal channel with a bottom width of 6 m....Ch. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Water is to be transported n a cast iron...Ch. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Prob. 55PCh. 13 - Prob. 56PCh. 13 - Prob. 58EPCh. 13 - Prob. 59EPCh. 13 - Prob. 60PCh. 13 - Repeat Prob. 13-60 for a weedy excavated earth...Ch. 13 - Prob. 62PCh. 13 - During uniform flow n open channels, the flow...Ch. 13 - Prob. 64PCh. 13 - Is it possible for subcritical flow to undergo a...Ch. 13 - How does nonuniform or varied flow differ from...Ch. 13 - Prob. 67CPCh. 13 - Consider steady flow of water; an upward-sloped...Ch. 13 - How does gradually varied flow (GVF) differ from...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. 73CPCh. 13 - Prob. 74CPCh. 13 - Water is flowing in a 90° V-shaped cast iron...Ch. 13 - Prob. 76PCh. 13 - Consider the flow of water through a l2-ft-wde...Ch. 13 - Prob. 78PCh. 13 - Prob. 79PCh. 13 - Prob. 80PCh. 13 - Prob. 81EPCh. 13 - Water flowing in a wide horizontal channel at a...Ch. 13 - Water discharging into a 9-m-wide rectangular...Ch. 13 - During a hydraulic jump in a wide channel, the...Ch. 13 - Prob. 92PCh. 13 - Prob. 93CPCh. 13 - Prob. 94CPCh. 13 - Prob. 95CPCh. 13 - Prob. 96CPCh. 13 - Prob. 97CPCh. 13 - Prob. 98CPCh. 13 - Consider uniform water flow in a wide rectangular...Ch. 13 - Prob. 100PCh. 13 - Prob. 101PCh. 13 - Prob. 102EPCh. 13 - Prob. 103PCh. 13 - Prob. 104PCh. 13 - Prob. 105PCh. 13 - Prob. 106EPCh. 13 - Prob. 107EPCh. 13 - Prob. 108PCh. 13 - Prob. 109PCh. 13 - Prob. 111PCh. 13 - Repeat Prob. 13-111 for an upstream flow depth of...Ch. 13 - Prob. 113PCh. 13 - Prob. 114PCh. 13 - Repeat Prob. 13-114 for an upstream flow depth of...Ch. 13 - Prob. 116PCh. 13 - Prob. 117PCh. 13 - Prob. 118PCh. 13 - Prob. 119PCh. 13 - Water flows in a canal at an average velocity of 6...Ch. 13 - Prob. 122PCh. 13 - A trapczoda1 channel with brick lining has a...Ch. 13 - Prob. 124PCh. 13 - A rectangular channel with a bottom width of 7 m...Ch. 13 - Prob. 126PCh. 13 - Prob. 128PCh. 13 - Prob. 129PCh. 13 - Consider o identical channels, one rectangular of...Ch. 13 - The flow rate of water in a 6-m-ide rectangular...Ch. 13 - Prob. 132EPCh. 13 - Prob. 133EPCh. 13 - Consider two identical 15-ft-wide rectangular...Ch. 13 - Prob. 138PCh. 13 - Prob. 139PCh. 13 - A sluice gate with free outflow is used to control...Ch. 13 - Prob. 141PCh. 13 - Prob. 142PCh. 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. 145PCh. 13 - Prob. 146PCh. 13 - Prob. 147PCh. 13 - Prob. 148PCh. 13 - Prob. 149PCh. 13 - Prob. 150PCh. 13 - Prob. 151PCh. 13 - Prob. 152PCh. 13 - Water f1ows in a rectangular open channel of width...Ch. 13 - Prob. 154PCh. 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 - Consider water flow in the range of 10 to 15 m3/s...
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- An 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_forwardSolve it correctly please. I will rate accordingly with 4votes.arrow_forwardThe head on a sharp-crested, rectangular weir was incorrectly observed to be 1.91 m. when it was actually 3.96 m. if the crest length is 4.57 meters, determine the percentage error (in percent) in the computed value of the flow rate Q. Use coefficient of discharge 0.945.arrow_forward
- 4. The discharge from a 150 mm diameter orifice under a head of 3.05m and coefficient of discharge, C = 0.60 flows into a rectangular channel and over a rectangular suppressed weir. The channel is 1.83m wide and the weir has height, P = 1,50m and length, L = 0.31m. Determine the depth of water in the channel. Use Francis formula and neglect velocity of approach.arrow_forwardA reservoir discharges through a sluice 0.915 m wide by 1.22 m deep. The top of the opening is 0.61 m below the water level in the reservoir and the downstream water level is below the bottom of the opening. Calculate (a) the discharge through the opening if Cg = 0.60 and (b) percentage error if the opening is treated as a small orifice. %3Darrow_forward2.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 applyarrow_forward
- Uniform water flow in a wide brick channel (n=0.015) of slope of 0.020 moves over a 10-cm bump as in Fig. 7a. A slight depression in water surface results. If the minimum water depth over the bump is 50 cm, compute the velocity over the bump and the flow rate per meter of width.arrow_forwardA constant head orifice from a tank feeds water into a flume (open channel) 5m in length and 500 mm wide with a rectangular contracted weir (L=200mm) at one end and close at the other end. The orifice diam is 80mm, coef of discharge= 0.92, and a head h=1m. c) Find the total time for the flow in the weir to stop after closing the supply of water from the orifice.arrow_forwardA reservoir has an outlet through a rectangular suppressed weir with a crest length of 1m. If its horizontal sectional area is constant at 1120 m?, how long will it take to lower the reservoir level from Elev. 5.00m to Elev. 4.80m if the crest is at Elev. 4.50m? Use the Francis Formula. O 81 s 321 s 501 s O 11 sarrow_forward
- A submerged sharp crested weir 0.81 m high stands clear across a channel having vertical sides and width of 3.15 m. The depth of water in the channel of approach is 1.26 m, and 10.5 m downstream from the weir the depth of water is 0.93 m. Determine the discharge in litres per minute. Assume Cd1 = 0.58 and Cd2 = 0.80.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_forwardWater 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-1arrow_forward
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