EBK WATER RESOURCES ENGINEERING
3rd Edition
ISBN: 9781119493167
Author: Mays
Publisher: VST
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Chapter 5, Problem 5.3.6P
To determine
The distance upstream of the dam where the normal depth occurs.
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Students have asked these similar questions
Example.
The discharge in a channel with bottom width 3 m is 12 m s. If Manning's n is 0.013
and the channel slope is 1 in 200, find the normal depth if:
the channel has vertical sides (i.e. rectangular channel):
(a)
(b)
the channel is trapezoidal with side slopes 2H:1V.
Consider a concrete (n=0.013) wide rectangular channel that discharges 2.0 m/sec per unit
bxh
width of the flow. The slope of the channel is 0.0001. A low dam causes a backwater depth
of 2.0 m immediately behind (upstream of) the dam.
Compute the distance upstream of the dam to where the normal depth occurs.
Ex. A small stream has a cross section which can be approximated by a trapezoid. The cross-sectional properties at three
sections are shown below. Section A is the downstream-most section. For a discharge of 100.0 m³/s in the stream, water surface
elevation at Section A was recorded as 104.5 m. Estimate the water-surface elevation at the upstream Section B and Section C.
Assume Manning's roughness n = 0.02 and energy coefficient a = 1.0 at all sections.
Section
A
B
C
Distance Up the River
(km)
100.00
102.00
103.50
Bed Elevation (m) Bed Width (m) Side Slope
100.000
14.0
1.5:1
100.800
12.5
1.5:1
101.400
10.0
1.5:1
Chapter 5 Solutions
EBK WATER RESOURCES ENGINEERING
Ch. 5 - Prob. 5.1.1PCh. 5 - Prob. 5.1.2PCh. 5 - Prob. 5.1.3PCh. 5 - Prob. 5.1.4PCh. 5 - Prob. 5.1.5PCh. 5 - Prob. 5.1.6PCh. 5 - Prob. 5.1.7PCh. 5 - Prob. 5.1.8PCh. 5 - Prob. 5.1.9PCh. 5 - Prob. 5.2.1P
Ch. 5 - Prob. 5.2.2PCh. 5 - Prob. 5.3.1PCh. 5 - Prob. 5.3.2PCh. 5 - Prob. 5.3.3PCh. 5 - Prob. 5.3.4PCh. 5 - Prob. 5.3.5PCh. 5 - Prob. 5.3.6PCh. 5 - Prob. 5.4.1PCh. 5 - Prob. 5.4.2PCh. 5 - Prob. 5.5.1PCh. 5 - Prob. 5.5.2PCh. 5 - Prob. 5.5.3PCh. 5 - Prob. 5.5.4PCh. 5 - Prob. 5.5.5PCh. 5 - Prob. 5.5.6P
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- The bottom width and bed slope of a long rectangular channel are 4.0 m and 0 0008, respectively. The volumetric steady-state discharge is 1.50 m/s. The flow depth at a specific location is 0 30 m. Ifn=0.016, determine: (a) The type of water surface profile expected Show all work and state your reasoning in support of your work Pleasell!! (b) Sketch the water surface profile with all necessary information and labels shownarrow_forwardLast two digit 30arrow_forwardWater flows at Q = 10 m³/s in a rectangular channel with b =4 m, n = 0.015, and So = 0.0009. If the flow depth at a gaging station is measured as 1 m, classify the gradually varied water surface profile, and use the differential equation of gradually varied flow to state whether the depth increases or decreases in the downstream direction. Assume the energy slope S/= 0.0025.arrow_forward
- A rectangular flume 2 m wide carries discharge at the rate of 2 m³/s. The bed slope of the flume is 0.0004. At a certain section the depth of flow is 1 m. Calculate the distance of the section downstream where the depth of flow is 0.9 m. Solve by single step method. Assume rugosity coefficient as 0.014. Is the slope of the channel mild or steep? How is this type of surface profile Classified ?arrow_forwardQ. No 1). Determine the discharge through a trapezoidal channel having X m base width, Side slope is 2:1 (Vertical to Horizontal). If the height of free surface of the water above the bed is 4 m. The bed slope is 1 in 1500, take n= 0.012. Width X=85arrow_forwardA rectangular channel 1.25m wide and 30m long with a flat bottom carries a flow of 0.5m3/s. The channel terminates in a free discharge. Plot a sketch of the water profile in the channel. Take n = 0.011. [10 Marks] b) Find the depth for uniform flow in a trapezoidal channel side slopes 1 in 2, and bottom width 3m, when the flow rate is 6m3/s if So = 0.0006 and n is assumed to be 0.016. Compute the corresponding value of e. [10 Marks]arrow_forward
- A trapezoidal is shown below. The particulars of the channel are as such: • Side slopes are 1 in 0.5 m. Manning's n = 0.015 • Slope of channel is 1 m in 1 km 0.5 b a. Using a value of 5 m for the bottom width and a normal depth of flow of 2 m, determin the following: i. ii. iii. Discharge Mean Velocity Reynolds No. b. If the discharge were 35 m³/s and bottom width was 5m, what would the normal depth of flow be? All other conditions remain the same.arrow_forwardConsider a 20-ft wide rectangular channel with a Manning's n value of 0.03. The channel has a discharge of 200 cubic feet per second at a uniform flow (normal) depth of 2 ft. A sluice gate at the downstream end of the channel controls the flow depth just upstream of the gate to a depth z. Determine the depth z so that a hydraulic jump is formed just upstream of the gate. What is the head loss (energy loss) in the hydraulic jump?arrow_forwardCalculate the discharge through the channel and the floodway (shown in the Figure below) for steady uniform flow, with S = 0.0009 and y = 8 ft. n=0.025 12 m 5 m n=0.040 POPSPAREN [Σ, Pn] + 120 m Side slopes 1:1 Use the following equivalent channel roughness formula due to Pavlovskii (1931)* ne = For 25,000 cfs flow through the channel above, find the depth of flow in the floodway when the slope of the energy grade line is 0.0004.arrow_forward
- Calculate the discharge through the channel and the floodway (shown in the Figure below) for steady uniform flow, with S = 0.0009 and y = 8 ft. n = 0.025 ne = 12 m 5 m n=0.040 √ [EXP²] + Р Paper 120 m ZAZ Use the following equivalent channel roughness formula due to Pavlovskii (1931)* Side slopes 1:1 For 25,000 cfs flow through the channel above, find the depth of flow in the floodway when the slope of the energy grade line is 0.0004.arrow_forwardThe discharge in a channel with bottom width 3 m is 12 m³ s¹. If Manning's n is 0.013 m-1/3 s and the streamwise slope is 1 in 200, find the normal depth if: (a) the channel has vertical sides (i.e. rectangular channel); (b) the channel is trapezoidal with side slopes 2H:1V.arrow_forwardPart 1 Water flows in a 5-ft-wide rectangular channel with a flowrate of Q = 30 ft/s and an upstream depth of y1 = 2.5 ft as shown in the figure below. Determine (a) the flow depth and (b) the surface elevation at section (2). Assume h2 = 0.2 ft. h, (2) (1) Concepts Bernoulli's equation applies along a streamline to frictionless flow Volume flowrate is constant for steady, incompressible flow There are two possible depths when the flow area changes in an open channel The Froude number indicates whether the flow is subcritical, critical, or supercritical (a) What is the velocity at section 1? i ft/s (b) What is the total energy of the flow at section 1, with the elevation of the bottom of the channel at section 1 as reference? ft (c) What is the Froude number of the flow at section 1? i (d) Is the flow at section 1 subcritical, critical, or supercritical?arrow_forward
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