Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.127P
To determine

i.

The normal depth of the river.

Expert Solution
Check Mark

Answer to Problem 10.127P

The normal depth of the river, yn = 2.21 ft.

Explanation of Solution

Given:

S0=0.0025

Q = 600 ft3 / s

b = 50 ft

increase in water depth = 8 ft

Concept:

Q=αnARh2/3So1/2

A=byn=50ynRh=bynb+2yn=50yn50+2ynForcleanearth,n=0.022Q=αnARh2/3So1/2600=1.4860.024(50yn)*( 50 y n 50+2 y n )2/3(0.0025)1/2yn=2.21ft

Conclusion:

The normal depth of the river is 2.21 ft.

To determine

ii.

The new water depth half mile upstream.

Expert Solution
Check Mark

Answer to Problem 10.127P

The new water depth half mile upstream is 1.4 ft.

Explanation of Solution

Given:

S0=0.0025

Q = 600 ft3 / s

b = 50 ft

y1 = 10 ft

Concept Used:

Foruniformflow,q=y1V1=y2V2E1=y1+V122gE2=y2+V222gSavg=n2Vavg2α2Rh,avg2SoSavg=E2E1Δx

Calculation:

Foruniformflow,Q=by1V1V1=Qby1V1=60050*10V1=1.2ft/sq=y1V1=y2V2V2=y1V1y2V2=0.24y2E1=y1+V122gE1=10+1.222*32.2E1=10.02ftE2=y2+V222gE2=y2+( 0.24 y 2 )22*32.2E2=y2+0.00089y22Vavg=V1+V22Vavg=1.2+0.24 y 22R1=by1b+2y1R1=50*1050+2*10R1=7.14ftR2=by2b+2y2R2=50y250+2y2

Rh,avg=R1+R22Rh,avg=7.143+50 y 250+2 y 22Savg=n2Vavg2α2Rh,avg2n=0.022Savg=0.0222( 1.2+ 0.24 y2 2 )21.4682( 7.143+ 50y2 50+2y2 2 )2Savg=0.000219(0.6 y 2+0.12 y 2)(50+2 y 2178.5+32.14 y 2)SoSavg=E2E1Δx0.0025[0.000219( 0.6 y 2 +0.12 y 2 )( 50+2 y 2 178.5+32.14 y 2 )]=y2+0.00089 y 2 210.020.5mi*5280ftmiy2=3.6ftThenewwaterdepth,Δy=y22.2Δy=3.62.2Δy=1.4ft.

Conclusion:

The new water depth half mile upstream is 1.4 ft.

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Chapter 10 Solutions

Fluid Mechanics

Ch. 10 - Prob. 10.11PCh. 10 - Prob. 10.12PCh. 10 - Prob. 10.13PCh. 10 - Prob. 10.14PCh. 10 - Prob. 10.15PCh. 10 - Prob. 10.16PCh. 10 - Prob. 10.17PCh. 10 - Prob. 10.18PCh. 10 - Prob. 10.19PCh. 10 - An unfinished concrete sewer pipe, of diameter 4...Ch. 10 - Prob. 10.21PCh. 10 - Prob. 10.22PCh. 10 - Prob. 10.23PCh. 10 - Prob. 10.24PCh. 10 - Prob. 10.25PCh. 10 - Prob. 10.26PCh. 10 - Prob. 10.27PCh. 10 - Prob. 10.28PCh. 10 - Prob. 10.29PCh. 10 - Prob. 10.30PCh. 10 - Prob. 10.31PCh. 10 - Prob. 10.32PCh. 10 - Prob. 10.33PCh. 10 - Prob. 10.34PCh. 10 - Prob. 10.35PCh. 10 - Prob. 10.36PCh. 10 - Prob. 10.37PCh. 10 - Prob. 10.38PCh. 10 - Pl0.39 A trapezoidal channel has n = 0.022 and Sn...Ch. 10 - Prob. 10.40PCh. 10 - Prob. 10.41PCh. 10 - Prob. 10.42PCh. 10 - Prob. 10.43PCh. 10 - Prob. 10.44PCh. 10 - Prob. 10.45PCh. 10 - Prob. 10.46PCh. 10 - Prob. 10.47PCh. 10 - Prob. 10.48PCh. 10 - Prob. 10.49PCh. 10 - Prob. 10.50PCh. 10 - Prob. 10.51PCh. 10 - Prob. 10.52PCh. 10 - Prob. 10.53PCh. 10 - A clay tile V-shaped channel has an included angle...Ch. 10 - Prob. 10.55PCh. 10 - Prob. 10.56PCh. 10 - Prob. 10.57PCh. 10 - Prob. 10.58PCh. 10 - Prob. 10.59PCh. 10 - Prob. 10.60PCh. 10 - P10.59 Uniform water flow in a wide brick channel...Ch. 10 - P10.62 Consider the flow in a wide channel over a...Ch. 10 - Prob. 10.63PCh. 10 - Prob. 10.64PCh. 10 - Prob. 10.65PCh. 10 - Prob. 10.66PCh. 10 - Prob. 10.67PCh. 10 - Prob. 10.68PCh. 10 - Given is the flow of a channel of large width b...Ch. 10 - Prob. 10.70PCh. 10 - Prob. 10.71PCh. 10 - Prob. 10.72PCh. 10 - Prob. 10.73PCh. 10 - Prob. 10.74PCh. 10 - Prob. 10.75PCh. 10 - Prob. 10.76PCh. 10 - Prob. 10.77PCh. 10 - Prob. 10.78PCh. 10 - Prob. 10.79PCh. 10 - Prob. 10.80PCh. 10 - Prob. 10.81PCh. 10 - Prob. 10.82PCh. 10 - Prob. 10.83PCh. 10 - Prob. 10.84PCh. 10 - Pl0.85 The analogy between a hydraulic jump and a...Ch. 10 - Prob. 10.86PCh. 10 - Prob. 10.87PCh. 10 - Prob. 10.88PCh. 10 - Prob. 10.89PCh. 10 - Prob. 10.90PCh. 10 - Prob. 10.91PCh. 10 - Prob. 10.92PCh. 10 - Prob. 10.93PCh. 10 - Prob. 10.94PCh. 10 - Prob. 10.95PCh. 10 - Prob. 10.96PCh. 10 - Prob. 10.97PCh. 10 - Prob. 10.98PCh. 10 - Prob. 10.99PCh. 10 - Prob. 10.100PCh. 10 - Prob. 10.101PCh. 10 - Prob. 10.102PCh. 10 - Prob. 10.103PCh. 10 - Prob. 10.104PCh. 10 - Prob. 10.105PCh. 10 - Prob. 10.106PCh. 10 - Prob. 10.107PCh. 10 - Prob. 10.108PCh. 10 - Prob. 10.109PCh. 10 - Prob. 10.110PCh. 10 - Prob. 10.111PCh. 10 - Prob. 10.112PCh. 10 - Prob. 10.113PCh. 10 - Prob. 10.114PCh. 10 - Prob. 10.115PCh. 10 - Prob. 10.116PCh. 10 - Prob. 10.117PCh. 10 - Prob. 10.118PCh. 10 - Prob. 10.119PCh. 10 - The rectangular channel in Fig. P10.120 contains a...Ch. 10 - Prob. 10.121PCh. 10 - Prob. 10.122PCh. 10 - Prob. 10.123PCh. 10 - Prob. 10.124PCh. 10 - Prob. 10.125PCh. 10 - Prob. 10.126PCh. 10 - Prob. 10.127PCh. 10 - Prob. 10.128PCh. 10 - Prob. 10.1WPCh. 10 - Prob. 10.2WPCh. 10 - Prob. 10.3WPCh. 10 - Prob. 10.4WPCh. 10 - Prob. 10.5WPCh. 10 - Prob. 10.6WPCh. 10 - Prob. 10.7WPCh. 10 - Prob. 10.8WPCh. 10 - Prob. 10.9WPCh. 10 - Prob. 10.10WPCh. 10 - Prob. 10.11WPCh. 10 - Prob. 10.12WPCh. 10 - Prob. 10.13WPCh. 10 - Prob. 10.1FEEPCh. 10 - Prob. 10.2FEEPCh. 10 - Prob. 10.3FEEPCh. 10 - Prob. 10.4FEEPCh. 10 - Prob. 10.5FEEPCh. 10 - Prob. 10.6FEEPCh. 10 - Prob. 10.7FEEPCh. 10 - February 1998 saw the failure of the earthen dam...Ch. 10 - Prob. 10.2CPCh. 10 - Prob. 10.3CPCh. 10 - Prob. 10.4CPCh. 10 - Prob. 10.5CPCh. 10 - Prob. 10.6CPCh. 10 - Prob. 10.7CPCh. 10 - Prob. 10.1DPCh. 10 - Prob. 10.2DP
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