Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11, Problem 6P
Capillary waves (ripples) are small amplitude and wavelength waves, commonly seen, for example, when an insect or small particle hits the water surface. They are waves generated due to the interaction of the inertia force of the fluid ρ and the fluid surface tension σ. The wavelength is
Find the speed of capillary waves in water and mercury.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
and w2 and
Two parallel traveling plane waves have different angular frequencies @1
pressure amplitudes P₁ and P₂. (a) Show that the instantaneous energy density %; at
a point in space varies between (P₁ + P₂)² / poc² and (P₁ – P₂)² / poc². (b) Show that
the total energy density & at the point averages to the sum of the individual energy
densities of each wave alone. Hint: Let the averaging time be much greater than
2πT/|w1 - w₂|.
The wave function for a wave on a taut string is given by
y(x,1)=0.35sin 10z1-3zx+-
where x and y are in meters and r is in seconds, The linear mass density of the string is u= 75.0 g/m,
(a) Calculate the speed of the traveling wave on the string.
(b) Calculate the average rate at which energy is transmitled along the string?
(c) Calculate the energy contained in each cycle of the wave?
A transverse wave in a string has the form y= 5 cos pi ( 0.02x +3.00 t), where x is in centimeters and t
is in seconds. The wave hits a stiff boundary and is reflected.
Derive an equation for the resulting standing waves.
Chapter 11 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 11 - Verify the equation given in Table 11.1 for the...Ch. 11 - A pebble is dropped into a stream of water that...Ch. 11 - Solution of the complete differential equations...Ch. 11 - A water flow rate of 250 cfs flows at a depth of 5...Ch. 11 - Determine and plot the relation between water...Ch. 11 - Capillary waves (ripples) are small amplitude and...Ch. 11 - The Froude number characterizes flow with a free...Ch. 11 - Consider waves on the surface of a tank of water...Ch. 11 - A submerged body traveling horizontally beneath a...Ch. 11 - Water flows in a rectangular channel at a depth of...
Ch. 11 - A partially open sluice gate in a 5-m-wide...Ch. 11 - Find the critical depth for flow at 3 m3/s in a...Ch. 11 - Flow occurs in a rectangular channel of 6 m width...Ch. 11 - What is the maximum flow rate that may occur in a...Ch. 11 - A rectangular channel carries a discharge of 10...Ch. 11 - Flow in the channel of Problem 11.15 has a...Ch. 11 - Consider the Venturi flume shown. The bed is...Ch. 11 - Eleven cubic meters per second of water are...Ch. 11 - A rectangular channel 10 ft wide carries 100 cfs...Ch. 11 - At what depths can 800 cfs flow in a trapezoidal...Ch. 11 - At a section of a 10-ft-wide rectangular channel,...Ch. 11 - Water, at 3 ft/s and 2 ft depth, approaches a...Ch. 11 - A horizontal rectangular channel 3 ft wide...Ch. 11 - A hydraulic jump occurs in a rectangular channel...Ch. 11 - A hydraulic jump occurs in a wide horizontal...Ch. 11 - A hydraulic jump occurs in a rectangular channel....Ch. 11 - The depths of water upstream and downstream from a...Ch. 11 - Calculate y2, h, and y3 for this two-dimensional...Ch. 11 - The hydraulic jump may be used as a crude flow...Ch. 11 - A hydraulic jump occurs on a horizontal apron...Ch. 11 - A hydraulic jump occurs in a rectangular channel....Ch. 11 - A positive surge wave, or moving hydraulic jump,...Ch. 11 - A 2-m-wide rectangular channel with a bed slope of...Ch. 11 - Determine the uniform flow depth in a rectangular...Ch. 11 - Determine the uniform flow depth in a trapezoidal...Ch. 11 - Water flows uniformly at a depth of 1.2 m in a...Ch. 11 - This large uniform open channel flow is to be...Ch. 11 - A rectangular flume built of timber is 3 ft wide....Ch. 11 - A channel with square cross section is to carry 20...Ch. 11 - A triangular channel with side angles of 45 is to...Ch. 11 - A flume of timber has as its cross section an...Ch. 11 - At what depth will 4.25 m3/s flow uniformly in a...Ch. 11 - A semicircular trough of corrugated steel, with...Ch. 11 - A rectangular flume built of concrete with 1 ft...Ch. 11 - Water flows in a trapezoidal channel at a flow...Ch. 11 - What slope is necessary to carry 11 m3/s uniformly...Ch. 11 - Find the normal depth for the channel of Problem...Ch. 11 - For a trapezoidal shaped channel with n = 0.014...Ch. 11 - Compute the critical depth for the channel in...Ch. 11 - A trapezoidal canal lined with brick has side...Ch. 11 - An optimum rectangular storm sewer channel made of...Ch. 11 - For a sharp-crested suppressed weir of length B =...Ch. 11 - A rectangular sharp-crested weir with end...Ch. 11 - What is the depth of water behind a rectangular...Ch. 11 - A broad-crested weir 0.9 m high has a flat crest...Ch. 11 - The head on a 90 V-notch weir is 1.5 ft. Determine...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
The value of ∂T/∂y and ∂T/∂x at surface B.
Introduction to Heat Transfer
A setup lake the one in Fig P3.108 has the R-410A initially at 1000 kPa, 50°C of mass 0.1 kg. The balancing equ...
Fundamentals Of Thermodynamics
Three rigid bodies, 2,3, and 4, are connected by four springs as shown in the figure. A horizontal force of 1,0...
Introduction To Finite Element Analysis And Design
The pipe assembly consists of three equal-sized pipes with flexibility stiffness EI and torsional stiffness GJ....
Mechanics of Materials
Determine the magnitude and coordinate direction angles of F2 so that the resultant of the three force is zero....
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
1.1 What is the difference between an atom and a molecule? A molecule and a crystal?
Manufacturing Engineering & Technology
Knowledge Booster
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
- Two simusoidal waves in a string are defined by the wave functions n = 2.00 sin(20.0r – 32.01) = 2.00 sin(25.0z - 40.01) where r, yi and y2 are in centimeters, t is in seconds and the angles are measured in radiaus. (a) What is the phase difference between these two waves at the point r 5.00 cm at t 2.00 s. Give your final answer in degrees between 0° and 360°. (b) What is the positive r value closest to the origin for which the two phases differ by +r at t= 2.00 s resulting in a zero displacement? Show all your workings and explain your reasoning.arrow_forward(C) A small-amplitude wave is progressing in the positive x-direction on the surface of water of constant density p and depth h, so that the equation of the surface is z = n(x, t) where z is measured vertically upwards from the undisturbed surface (z = 0). = e sin(kx - wt) with € < 1, the pressure in the fluid can be You are given that for n(x, t) written P= Papgz + po, where Pa is the constant atmospheric pressure and is given by = eg sin(kx - wt) cosh[k(z + h)]/cosh(kh). Here k and w are related through the dispersion relation c = gk tanh kh. Consider the form of this flow in the shallow water limit, kh → 0. 1. What is the dispersion relation in this limit? 2. What is the wave speed? 3. Show that to leading order in kh the horizontal component of velocity is the same at all depths. 4. Show that to leading order in kh the vertical component of velocity varies linearly with depth, satisfying the kinematic boundary conditions on y = 0 and y = :-h.arrow_forwardA traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), wherex and y are in meters and t is in seconds. %3D The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same frequency, and same linear mass density, then the new power of the wave, is O 500 W 125 W 1000 W 250 W 2000 W The wovefunction of a mechanical wave on a string is described by: y(x.t) =arrow_forward
- The equation of a wave in the international system SI, which propagates by a string is given by the expression: y(x,t)=0,08cos[2π(2x-4t)] Determine the velocity values at a point 2m from the source at the instant t=5s.arrow_forwardA 2-m sea wave has a 6 s period and occurs at the surface of 100-m deep water. Assume sea- water density equals to 1,025 kg/m³. Calculate the energy and power densities of the wave.arrow_forwardA traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same wavelength, and same !! linear mass density, then the new power of the wave, isarrow_forward
- A sinusoidal wave of height of 5 feet is propagating to the "right" in sea-water of depth of 100 feet with a celerity of 30 ft/sec. At a location A under the free surface the diameter of the circular particle trajectories has been found to be equal to 23 inches. Determine the following: a) The period and length of this wave. Assume deep water, and then verify this assumption.arrow_forwardSomewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d^2x/dt^2=-(pi^2/36)x. Here x refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m=3kg. The length of the string is given by L=5 meters. Whenever the particle arrives at a location of x=(pi/12) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, x=(pi/12) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. 1. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. 2. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? 3. Approximating…arrow_forward1. You hear a sonic boom and immediately look up to see where the plane is. Instead of a plane, you see an alien spacecraft 55° above the horizon. V sound sin a = Vsource (a) How fast is the alien spacecraft traveling? (b) If the alien spacecraft has an altitude of 6000 m, how long ago did it pass overhead? (c) Draw a picture of the soundwaves emitted by the alien spacecraft. Mark the interference that creates the shockwave.arrow_forward
- A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(2TTX-300t)., where x and y are in meters and t is in seconds. The linear mass density of the string is u = 100 g/m. and the string is 10 m-long. The total energy on the string is O 90 J 450 J 22.5 J 225 J 45 J Back Submit Page 2 of 2 Never submit pasowords through Google Forms. This form was created insidel of Lebeneetac a er SeantAoueSarrow_forwardA traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same frequency, and same linear mass density, then the new power of the wave, is 1000 W O 2000 W O 250 W O 500 W 125 Warrow_forwardDevelop an equation for the transmitted wave height behind a vertical wall extending a depth d into the water of depth h, based on the concept that the wall allows the wave power below depth d to propagate past. Qualitatively, do you believe that your equation for the transmitted wave height will under- or overestimate the actual wave height ? Discuss your results.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
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