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 62P
To determine
The flow rate when some algae growth on surfaces whiles the flow cross -section remains constant.
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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
A 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.
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
41
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Gradually varied flow of water in a wide rectangular channel with a per-unitwidth flow rate of 1 m3/s⋅m and a Manning coefficient of n = 0.02 is considered. The slope of the channel is 0.001, and at the location x = 0, the flow depth is measured to be 0.8 m. (a) Determine the normal and critical depths of the flow and classify the water surface profile, and (b) calculate the flow depth y at x = 1000 m by integrating the GVF equation numerically over the range 0 ≤ x ≤ 1000 m. Repeat part (b) to obtain the flow depths for different x values, and plot the surface profile.arrow_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_forwardWater flows in a channel whose bottom slope is 0.002 and whose cross section is as shown. The dimensions and the Manning coefficients for the surfaces of different subsections are also given on the figure. Determine the flow rate through the channel and the effective Manning coefficient for the channel.arrow_forward
- Consider the uniform flow of water in the triangular channel shown in the figure. The channel bed slope is 0.003 and the roughness coefficient is 0.025. The flow rate in the channel is 25 m³/s. What is the normal depth? a.3.48 m b.2.28 m c.4.70 m d. 1.98 m What is the critical depth? a. 1.98 m b.4.70 m c.3.48 m d.2.28 m If the flow depth at a certain section of the channel is 2 m, the flow is: a.subcritical b.critical c.supercritical d.can not be determined VAI 2 1arrow_forward2) A venturi flume is placed near the middle of a long rectangular channel with Manning's coefficient n= 0.012 m s. The channel has a width of 5 m, a discharge of 12.5 m's" and a slope of 1:2500. (a) Determine the critical depth and the normal depth in the main channel. (b) Determine the venturi flume width which will just make the flow critical at the contraction. (c) If the contraction width is 2 m find the depths just upstream, downstream and at the throat of the venturi flume (neglecting friction in this short section). (d) Sketch the surface profile.arrow_forwardThe best hydraulic cross section for a rectangular open channel is one whose fluid height is (a) half, (b) twice, (c) equal to, or (d) one-third the channel width.arrow_forward
- 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.arrow_forwardWater (p = 999.1ku = 1.13 x 10-3 k) in a 6-m-wide rectangular channel at a %3D depth of 1 m and a flow rate of 10 m/s. Determine: (1) the Froude Number; (2) whether the flow is subcritical or supercritical; (3) critical depth, critical velocity, critical energy; (4) specific energy.arrow_forwardConsider gradually varied flow of water in a 20-ft wide rectangular channel with a flow rate of 300ft3/s and a Manning coefficient of 0.008. The slope of the channel is 0.01, and at the location x = 0, the mean flow speed is measured to be 5.2ft/s. Determine the classification of the water surface profile, and, by integrating the GVF equation numerically, calculate the flow depth y at (a) x = 500ft, (b) 1000ft, and (c) 2000ft.arrow_forward
- A sluice gate with free outflow is used to control the discharge rate of water through a channel. Determine the flow rate per unit width when the gate is raised to yield a gap of 50 cm and the upstream flow depth is measured to be 2.8 m . Also determine the flow depth and the velocity downstreamarrow_forwardWater is flowing uniformly in a rectangular open channel with unfinished-concrete surfaces. The channel width is 6 m, the flow depth is 2 m, and the bottom slope is 0.004. Determine if the channel should be classified as mild, critical, or steep for this flowarrow_forwardWater is to be transported in a finished-concrete rectangular channel with a bottom width of 1.2 m at a rate of 5 m3 /s. The channel bottom drops 1 m per 500 m length. The minimum height of the channel under uniform-flowconditions is(a) 1.9 m (b) 1.5 m (c) 1.2 m (d) 0.92 m (e) 0.60 marrow_forward
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