Fluid Mechanics: Fundamentals and Applications
Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 13, Problem 128P
To determine

The velocity before the jump.

The velocity after the jump.

The mechanical power dissipated.

Expert Solution & Answer
Check Mark

Answer to Problem 128P

The velocity before the jump is 14.132m/s.

The velocity after the jump is 1.978m/s.

The mechanical power dissipated is 559.5787kW.

Explanation of Solution

Given information:

The flow depth before the jump is 0.7m, the flow depth after the jump is 5m, the flow is steady and uniform and the end effect is neglected.

Write the expression for flow depth.

  y2=0.5y1(1+1+8 Fr12)....... (I)

Here, Froude number is Fr1, height before jump is y1, height after the jump is y2.

Write the expression for Froude number.

  Fr=V1gy1...... (II)

Here, acceleration due to gravity is g and velocity before jump is V1.

Write the expression for conservation of mass.

  y1V1=y2V2...... (III)

Here, velocity after jump is V2.

Write the expression for volume flow rate.

  V˙=V1by1...... (IV)

Write the expression for head loss during the jump.

  hL=y1y2+V12V222g...... (V)

Write the expression for mass flow rate.

  m˙=ρV˙...... (VI)

Here, density of water is ρ.

Write the expression for energy dissipated.

  E˙dissipated=m˙ghL...... (VII)

Calculation:

Substitute 0.7m for y1, 5m for y2 in Equation (I).

  5m=0.5(0.7m)(1+ 1+8 Fr 1 2 )(1+ 1+8 Fr 1 2 )=10m0.7m1+8 Fr12=15.2861+8Fr12=233.662Fr12=29.083

  Fr=5.393

Substitute 0.7m for y1, 5.393 for Fr and 9.81m/s2 for g in Equation (II).

  5.393=V1 9.81m/ s 2 ×0.7mV1=(5.393)9.81m/ s 2×0.7mV1=14.132m/s

Substitute 0.7m for y1, 5m for y2 and 14.132m/s for V1 in Equation (III).

  (0.7m)(14.132m/s)=(5m)V2V2=0.7m5m×14.132m/sV2=1.978m/s

Substitute 0.7m for y1, 14.132m/s for V1 and 1m for b in Equation (IV).

  V˙=(14.132m/s)(1m)(0.7m)=14.132m/s×0.7m2=9.892m3/s

Substitute 0.7m for y1, 5m for y2 and 14.132m/s for V1, 1.978m/s for V2 and 9.81m/s2 for g in Equation (V).

  hL=(0.7m)(5m)+ ( 14.132m/s )2 ( 1.978m/s )22( 9.81m/ s 2 )=4.3m+ ( 14.132m/s )2 ( 1.978m/s )219.62m/ s 2=5.778m

Refer to table "Liquid water at 20°C " to obtain density of water as 998kg/m3.

Substitute 998kg/m3 for ρ and 9.892m3/s for V˙ in Equation (VI).

  m˙=(998kg/ m 3)(9.892 m 3/s)=9872.216kg/s

Substitute 9872.216kg/s for m˙, 5.68m for hL and 9.81m/s2 for g in Equation (VII).

  E˙dissipated=(9872.216kg/s)(9.81m/ s 2)(5.778m)=559.5787×103kgm2/s3×1W1 kg m 2 /s 3=559.5787×103W×1kW1000W=559.5787kW

Conclusion:

The velocity before the jump is 14.132m/s.

The velocity after the jump is 1.978m/s.

The mechanical power dissipated is 559.5787kW.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
The flow depth and velocity of water after undergoing a hydraulic jump are measured to be 1.1 m and 1.75 m/s, respectively. Determine the flow depth and velocity before the jump, and the fraction of mechanical energy dissipated.
The specific energy for a 3 m wide channel is to be 3 kg-m/kg. What would be the maximum possible discharge?
A sluice gate with free outflow is used to control the discharge rate of water through a channel. Determine the flow rate per unit width when the gate is raised to yield a gap of 50 cm and the upstream flow depth is measured to be 2.8 m . Also determine the flow depth and the velocity downstream

Chapter 13 Solutions

Fluid Mechanics: Fundamentals and Applications

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...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
8.01x - Lect 27 - Fluid Mechanics, Hydrostatics, Pascal's Principle, Atmosph. Pressure; Author: Lectures by Walter Lewin. They will make you ♥ Physics.;https://www.youtube.com/watch?v=O_HQklhIlwQ;License: Standard YouTube License, CC-BY
Dynamics of Fluid Flow - Introduction; Author: Tutorials Point (India) Ltd.;https://www.youtube.com/watch?v=djx9jlkYAt4;License: Standard Youtube License