Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.66P
To determine

(a)

If the water will rise above the bump.

Expert Solution
Check Mark

Answer to Problem 10.66P

The water level increases over the bump since it is super critical flow.

Explanation of Solution

Given:

Velocity V1 = 5.5 m/s

y1 = 90cm

Concept Used:

Point1isattheflowbeforethebump.Ponit2isabovethebumpFr=VVc

Calculation:

Point1isattheflowbeforethebump.Ponit2isabovethebumpFr1=V1V1c5.5gy15.59.81*0.9Fr1=1.85SIncetheFroudenumberisgreaterthan1.Theflowissupercritical.Therfore,thewaterincreasesoverthebump

Conclusion:

The water level increases over the bump.

To determine

(b)

The Froude number over the bump if bump height is 30 cm.

Expert Solution
Check Mark

Answer to Problem 10.66P

The Froude number over the bump is 1.388

Explanation of Solution

Given:

Velocity V1 = 5.5 m/s

y1 = 90 cm

Bump height = 30cm

Concept Used:

Point1isattheflowbeforethebump.Ponit2isabovethebumpy2=initialheight+bumpheightFr=VVc

Calculation:

Point1isattheflowbeforethebump.Ponit2isabovethebumpForuniformflow,q=y1V1=y2V2E2=V122g+y1ΔhE2=5.522*9.81+0.90.3E2=2.141my23E2y22+q22g=0y232.141y22+(0.9*5.5)22*9.81=0Onsolvingfory2,wegety2=1.09mFrbump=V2V2cy1V1y2gy20.9*5.51.099.81*1.09Frbump=1.388

Conclusion:

The Froude number over the bump is 1.388.

To determine

(c)

The bump height that will cause critical flow.

Expert Solution
Check Mark

Explanation of Solution

Given:

Velocity V1 = 5.5 m/s

y1 = 90 cm

Concept Used:

Δh=E1E2ΔhistheheightofthebumpE=V22g+yEc=32ycyc=(q2g)1/3

Calculation:

Δh=E1E2ΔhistheheightofthebumpE1=V122g+y1E1=5.522*9.81+0.9E1=2.441Forenergywithcriticalflow,E2=32ycE2=32(q2g)1/3E2=32((5.5*0.9)29.81)1/3E2=2.02mΔh=E1E2Δh=2.4112.02Δh=0.42m

Conclusion:

The Froude number over the bump is 1.37.

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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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