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 63P
During uniform flow n open channels, the flow velocity and the flow rate can be determined from the Manning equations expressed as
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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.
a)Water at 20 °C flows in a partially full 2 m diameter circular channel at an average velocity of 2 m/s. If the maximum water depth is 0.5 m, determine the hydraulic radius, the Reynolds number, and the flow regime.
b) The flow rate of water through a 5 m wide (into the paper) channel is controlled by a sluice gate. If the flow depths are measured to be 1.1 and 0.45 m upstream and downstream from the gates, respectively, determine the flow rate and the Froude number downstream from the gate.
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.
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
- For sluice gates, how is the discharge coefficient Cd defined? What are typical values of Cd for sluice gates with free outflow? What is the value of Cd for the idealized frictionless flow through the gate?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_forwardWater discharging into a 10-m-wide rectangular horizontal channel from a sluice gate is observed to have undergone a hydraulic jump. The flow depth and velocity before the jump are 0.8 m and 7 m/s, respectively. Determine (a) the flow depth and the Froude number after the jump, (b) the head loss and the energy dissipation ratio, and (c) the wasted power production potential due to the hydraulic jumparrow_forward
- Water at 20°C flows in a partially full 4-m-diameter circular channel at an average velocity of 2 m/s. If the maximum water depth is 1 m, determine the hydraulic radius, the Reynolds number, and the flow regime.arrow_forwardDuring steady and uniform flow through an open channel of rectangular cross section, a person claims that the specific energy of the fluid remains constant. A second person claims that the specific energy decreases along the flow because of the frictional effects and thus head loss. With which person do you agree? Explain.arrow_forwardWhat is the significance of the Determination of the coefficient of discharge of a 90-degree triangular notch weir experiment?arrow_forward
- Water flows in a rectangular channel with a width of 2.5 m. The kinetic energy correction coefficient (i.e. velocity coefficient) is estimated as a = 1.2. If the flow rate is 5 m³/s and the flow depth is 1.5 m: (a) determine the specific energy of the flow. (b) Calculate the alternate depth considering α = 1.0.arrow_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_forwardA channel has a slope of 0.0004 m/m with n=0.015. It is expected that the channel will be able to carry a flow rate of 50 m3/s. Determine the normal depth, critical depth, critical slope,hydraulic radius, top width, velocity head, specific energy and the state of flow if the channel section is trapezoidal and its base width is 3.056 m. The side walls make an angle of 45 with horizontal level. Take ρ=1000 kg/m3 and g = 9.81 m/s2 Froude Number is estimated from F(r^2)=(V^2)T/g(A^3)arrow_forward
- The flow rate of water flowing in a 5-m-wide channel is to be measured with a sharp-crested triangular weir 0.5 m above the channel bottom with a notch angle of 80°. If the flow depth upstream from the weir is 1.5 m, determine the flow rate of water through the channel. Take the weir discharge coefficient to be 0.60.arrow_forwardHow is the specific energy of a fluid flowing in an open channel defined in terms of heads?arrow_forwardConsider uniform water flow in a wide rectangular channel with a depth of 2 m made of unfinished concrete laid on a slope of 0.0022. Determine the flow rate of water per meter width of channel. Now water flows over a 15-cm-high bump. If the water surface over the bump remains flat (no rise or drop), determine the change in discharge rate of water per meter width of the channel.arrow_forward
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