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

Videos

Question
Book Icon
Chapter 13, Problem 100P
To determine

The change in water level.

Whether the flow over the bump is sub or supercritical.

Expert Solution & Answer
Check Mark

Answer to Problem 100P

The rise in water level over the bump is 0.322m.

The flow over the bump is supercritical.

Explanation of Solution

Given information:

Velocity of water flow is 10m/s, the flow depth is 0.65m, the bump height is 30cm.

Write the expression for the Froude number.

  Fr1=V1gy1  ...... (I)

Here, the velocity of fluid is V1 the acceleration due to gravity is g and the fluid depth before the bump is y1.

The figure below shows the rise over the bump.

  Fluid Mechanics: Fundamentals and Applications, Chapter 13, Problem 100P

  Figure-(1)

Write the expression for the critical flow depth.

  yc=( V 1 2 y 1 2 g)1/3....... (II)

Write the expression for the specific energy before the bump.

  Es1=y1+V22g  ...... (III)

Write the expression for the specific energy over the bump.

  Es2=Es1Δzb  ...... (IV)

Here, the height of the bump is Δzb.

Write the expression for the critical specific energy.

  Ec=32yc  ...... (V)

Here the critical flow depth is yc

Write the expression to calculate the flow over the bump.

  y23(Es1Δzb)y22+V122gy12=0  ...... (VI)

Here, the specific energy before the bump is Es1, the specific energy over the bump is Es2, the flow depth before the bump is y1 and the flow depth over the bump is y2.

Write the expression for the rise over the bump.

  Bs=y2y1+Δzb  ...... (VII)

Calculation:

Substitute 10m/s for V1

  9.81m/s2 for g and 0.65m for y1 in Equation (I).

  Fr1=10m/s ( 9.81m/ s 2 )×( 0.65m )=10m/s ( 6.3765 m 2 / s 2 )=10m/s2.525m/s=3.960

The Froude number is greater than 1 hence the flow is supercritical before the bump.

Substitute 10m/s for V1, 9.81m/s2 for g

  0.65m for y1 in Equation (II).

  yc=( ( 10m/s ) 2 × ( 0.65m ) 2 9.81m/ s 2 )1/3=( ( 100 m 2 / s 2 )×( 0.4225 m 2 ) 9.81m/ s 2 )1/3=( ( 42.25 m 4 / s 2 ) 9.81m/ s 2 )1/3=(4.3068 m 3)1/3

  yc=1.62699m

Substitute 10m3/s for V, 0.65m for y1 and 9.81m/s2 for g in Equation (III).

  Es1=0.65m+ ( 10m/s )22( 9.81m/ s 2 )=0.65m+5.096m=5.74m

Substitute 5.74m for Es1 and 0.3m for Δzb in Equation (IV).

  Es2=5.74m0.3m=5.44m

Substitute 1.62994m for yc in Equation (V).

  Ec=32(1.62994m)=2.44m

Substitute 5.74m for Es1, 0.3m for Δzb, 10m/s for V1

  0.65m for y1 and 9.81m/s2 in Equation (VI).

  y23(5.74m0.3m)y22+ ( 10m/s )22( 9.81m/ s 2 )(10m)2=0y235.44y222.153=0

After solving by iteration method three roots of the y2 are 5.372m, 0.597m and 0.672m.

A physical meaningful root of the equation is 0.672m.

Substitute 0.3m for Δzb, 0.65m for y1, and 0.672m for y2 in Equation (VII).

  Bs=0.672m0.65m+0.30m=0.022m0.30m=0.322m

Substitute 10m/s for V1

  9.81m/s2 for g and 0.322m for y1 in Equation (I).

  Fr1=10m/s ( 9.81m/ s 2 )×( 0.322m )=10m/s ( 3.15882 m 2 / s 2 )=10m/s1.777m/s=5.626

The Froude number is greater than 1 hence the flow is supercritical over the bump.

Conclusion:

The rise in water level over the bump is 0.322m.

The flow over the bump is supercritical.

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
Water flowing in a wide channel encounters a 22-cm-high bump at the bottom of the channel. If the flow depth is 1.2 m and the velocity is 2.5 m/s before the bump, determine if the flow is choked over the bump, and discuss.
Water at 15°C is flowing uniformly in a 2-m-wide rectangular channel at an average velocity of 1.5 m/s. If the water depth is 24 cm, determine whether the flow is subcritical or supercritical.
Water is flowing uniformly in a finished-concrete channel of trapezoidal cross section with a bottom width of 0.8 m, trapezoid angle of 50°, and a bottom angle of 0.4°. If the flow depth is measured to be 0.52 m, determine the flow rate of water through the channel.

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
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License