To determine Two possible flow depths. Explanation Write the expression of the flow rate per width. q = Q b (I) Here, the volumetric flow rate is Q and the width of the rectangular channel is b . Write the expression of specific energy for the rectangular channel. E = q 2 2 g y 2 + y (II) Here, the depth of rectangle is y , unit discharge is q , and gravitational acceleration is g . Conclusion: Substitute 10 ft for b and 200 ft 3 / s for Q in Equation (I). q = ( 200 ft 3 / s ) ( 10 ft ) = 20 ft 2 / s Substitute 20 ft 2 / s for q , 6 ft for E and 32.17 ft / s 2 for g in Equation (II) 6 ft = ( 20 ft 2 / s ) 2 2 × ( 32.17 ft / s 2 ) × y 2 + y ( 6 ft ) y 2 = ( 6.217 ft 3 ) + y 3 y 3 − ( 6 ft ) y 2 + ( 6.217 ft 3 ) = 0 Solving the above cubic equation and obtaining the roots of the cubic Equation. y 1 = 5.816 ft y 2 = 1.129 ft y 3 = − 0.946 ft As the depth cannot be negative, two possible flow depths for the rectangular channel are 5.816 ft and 1.129 ft . Substitute 20 ft 2 / s for q and 32.17 ft / s 2 for g in Equation (II) E = ( 20 ft 2 / s ) 2 2 × ( 32.17 ft / s 2 ) × y 2 + y E = ( 6.217 ft 3 ) y 2 + y (III) Substitute 1 ft for y in Equation (III)

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 10.3, Problem 13P

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Two possible flow depths.

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Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

Ch. 10.2 - Prob. 1P Ch. 10.2 - The flowrate per unit width in a wide channel is q...Ch. 10.2 - A rectangular channel 3 m wide carries 10 m3/s at...Ch. 10.2 - Prob. 4P Ch. 10.2 - Prob. 5P Ch. 10.2 - Prob. 6P Ch. 10.2 - Prob. 7P Ch. 10.2 - Prob. 8P Ch. 10.2 - Prob. 9P Ch. 10.2 - Prob. 10P

Ch. 10.2 - Prob. 11P Ch. 10.3 - Water flows in a 10-m-wide open channel with a...Ch. 10.3 - Water flows in a 10-ft-wide rectangular channel...Ch. 10.3 - Water flows in a rectangular channel at a rate of...Ch. 10.3 - Water flows in a 5-ft-wide rectangular channel...Ch. 10.3 - Water flows over the bump in the bottom of the...Ch. 10.3 - Water in a rectangular channel flows into a...Ch. 10.3 - A channel has a rectangular cross section, a width...Ch. 10.3 - Prob. 19P Ch. 10.3 - Prob. 20P Ch. 10.3 - Prob. 23P Ch. 10.3 - Prob. 24P Ch. 10.3 - Prob. 25P Ch. 10.3 - Prob. 26P Ch. 10.3 - Prob. 27P Ch. 10.3 - Prob. 28P Ch. 10.3 - Prob. 29P Ch. 10.4 - Water flows in a 5-m-wide channel with a speed...Ch. 10.4 - The following data are taken from measurements on...Ch. 10.4 - Prob. 32P Ch. 10.4 - The following data are obtained for a particular...Ch. 10.4 - Prob. 34P Ch. 10.4 - Prob. 35P Ch. 10.4 - A 2-m-diameter pipe made of finished concrete lies...Ch. 10.4 - By what percent is the flowrate reduced in the...Ch. 10.4 - Prob. 38P Ch. 10.4 - Prob. 39P Ch. 10.4 - Prob. 40P Ch. 10.4 - A trapezoidal channel with a bottom width of 3.0 m...Ch. 10.4 - Water flows in a 2-m-diameter finished concrete...Ch. 10.4 - A round concrete storm sewer pipe used to carry...Ch. 10.4 - Find the discharge per unit width for a wide...Ch. 10.4 - Water flows down a wide rectangular channel having...Ch. 10.4 - Prob. 46P Ch. 10.4 - Prob. 47P Ch. 10.4 - Prob. 48P Ch. 10.4 - Determine the flowrate for the symmetrical channel...Ch. 10.4 - (See The Wide World of Fluids article titled “Done...Ch. 10.4 - Prob. 51P Ch. 10.4 - Prob. 52P Ch. 10.4 - Prob. 53P Ch. 10.4 - Prob. 54P Ch. 10.4 - Prob. 55P Ch. 10.4 - Prob. 56P Ch. 10.4 - Prob. 57P Ch. 10.4 - Prob. 58P Ch. 10.4 - Prob. 59P Ch. 10.4 - Prob. 60P Ch. 10.4 - Prob. 61P Ch. 10.4 - Prob. 62P Ch. 10.4 - Prob. 63P Ch. 10.4 - Water flows 1 m deep in a 2-m-wide finished...Ch. 10.4 - Uniform flow in a sluggish channel having a nearly...Ch. 10.4 - To prevent weeds from growing in a clean...Ch. 10.4 - Prob. 67P Ch. 10.4 - Prob. 68P Ch. 10.4 - Prob. 69P Ch. 10.4 - Prob. 70P Ch. 10.5 - Prob. 71P Ch. 10.5 - Prob. 72P Ch. 10.6 - Water flows upstream of a hydraulic jump with a...Ch. 10.6 - Prob. 75P Ch. 10.6 - Prob. 76P Ch. 10.6 - Prob. 77P Ch. 10.6 - At a given location in a 12-ft-wide rectangular...Ch. 10.6 - Prob. 79P Ch. 10.6 - Prob. 80P Ch. 10.6 - Prob. 81P Ch. 10.6 - A hydraulic engineer wants to analyze steady flow...Ch. 10.6 - Prob. 83P Ch. 10.6 - A rectangular sharp-crested weir is used to...Ch. 10.6 - Prob. 85P Ch. 10.6 - Prob. 87P Ch. 10.6 - Prob. 88P Ch. 10.6 - Prob. 89P Ch. 10.6 - Prob. 90P Ch. 10.6 - Prob. 91P Ch. 10.7 - Prob. 1LLP Ch. 10.7 - Prob. 2LLP Ch. 10.7 - Prob. 3LLP

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