Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 7, Problem 14P
The speed, V, of a free-surface wave in shallow liquid is a function of depth, D, density, ρ, gravity, g, and surface tension, σ. Use dimensional analysis to find the functional dependence of V on the other variables. Express V in the simplest form possible.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance
through the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure
p, and the water viscosity μ. You want to find a set of dimensionless variables on which the thrust coefficient
depends. In other words
CT =
FT
· = ƒen(#1, #2, ...)
pV2D2
(a) What is k? Explain.
(b) Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V²,
(1)
1ODiem #
The side thrust F, for a smooth spinning ball in a fluid is a function of the
ball diameter D, the free-stream velocity V, the densityp, the viscosityu,
and the angular velocity of spino.
F= f( D, ρ, μ, V, ω)
Using the Buckingham Pi theorem to express this relation in dimensionless
form.
F
The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.
Chapter 7 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 7 - The slope of the free surface of a steady wave in...Ch. 7 - One-dimensional unsteady flow in a thin liquid...Ch. 7 - In atmospheric studies the motion of the earths...Ch. 7 - Fluid fills the space between two parallel plates....Ch. 7 - By using order of magnitude analysis, the...Ch. 7 - Consider a disk of radius R rotating in an...Ch. 7 - An unsteady, two-dimensional, compressible,...Ch. 7 - Experiments show that the pressure drop for flow...Ch. 7 - At very low speeds, the drag on an object is...Ch. 7 - We saw in Chapter 3 that the buoyant force, FB, on...
Ch. 7 - Assume that the velocity acquired by a body...Ch. 7 - Derive by dimensional analysis an expression for...Ch. 7 - The speed of shallow water waves in the ocean...Ch. 7 - The speed, V, of a free-surface wave in shallow...Ch. 7 - The boundary-layer thickness, , on a smooth flat...Ch. 7 - The speed, V, of a free-surface gravity wave in...Ch. 7 - Derive an expression for the velocity of very...Ch. 7 - Derive an expression for the axial thrust exerted...Ch. 7 - Derive an expression for drag force on a smooth...Ch. 7 - The energy released during an explosion, E, is a...Ch. 7 - Measurements of the liquid height upstream from an...Ch. 7 - The load-carrying capacity, W, of a journal...Ch. 7 - Derive an expression for the drag force on a...Ch. 7 - A circular disk of diameter d and of negligible...Ch. 7 - Two cylinders are concentric, the outer one fixed...Ch. 7 - The time, t, for oil to drain out of a viscosity...Ch. 7 - You are asked to find a set of dimensionless...Ch. 7 - A continuous belt moving vertically through a bath...Ch. 7 - Derive an expression for the frictional torque...Ch. 7 - Tests on the established flow of six different...Ch. 7 - The power, P, required to drive a fan is believed...Ch. 7 - The sketch shows an air jet discharging...Ch. 7 - The diameter, d, of bubbles produced by a...Ch. 7 - Choked-flow nozzles are often used to meter the...Ch. 7 - A large tank of liquid under pressure is drained...Ch. 7 - Spin plays an important role in the flight...Ch. 7 - The power loss, P, in a journal bearing depends on...Ch. 7 - The thrust of a marine propeller is to be measured...Ch. 7 - The rate dT/dt at which the temperature T at the...Ch. 7 - When a valve is closed suddenly in a pipe with...Ch. 7 - An airship is to operate at 20 m/s in air at...Ch. 7 - An airplane wing of 3 m chord length moves through...Ch. 7 - A flat plate 1.5 m long and 0.3 m wide is towed at...Ch. 7 - This 1:12 pump model using water at 15C simulates...Ch. 7 - An ocean-going vessel is to be powered by a...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - A 1:3 scale model of a torpedo is tested in a wind...Ch. 7 - A flow rate of 0:18 m3/s of water at 20C...Ch. 7 - A force of 9 N is required to tow a 1:50 ship...Ch. 7 - An airplane wing, with chord length of 1.5 m and...Ch. 7 - A water pump with impeller diameter of 24 in. is...Ch. 7 - A model hydrofoil is to be tested at 1:20 scale....Ch. 7 - A ship 120 m long moves through freshwater at 15C...Ch. 7 - A 1:30 scale model of a cavitating overflow...Ch. 7 - In some speed ranges, vortices are shed from the...Ch. 7 - A 1:8 scale model of a tractor-trailer rig is...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - When a sphere of 0.25 mm diameter and specific...Ch. 7 - The flow about a 150 mm artillery projectile which...Ch. 7 - Your favorite professor likes mountain climbing,...Ch. 7 - A 1:50-scale model of a submarine is to be tested...Ch. 7 - Consider water flow around a circular cylinder, of...Ch. 7 - A 1:10 scale model of a tractor-trailer rig is...Ch. 7 - The power, P, required to drive a fan is assumed...Ch. 7 - Over a certain range of air speeds, V, the lift,...Ch. 7 - The pressure rise, p, of a liquid flowing steadily...Ch. 7 - An axial-flow pump is required to deliver 0.75...Ch. 7 - A model propeller 1 m in diameter is tested in a...Ch. 7 - Consider Problem 7.38. Experience shows that for...Ch. 7 - Closed-circuit wind tunnels can produce higher...Ch. 7 - A 1:16 model of a bus is tested in a wind tunnel...Ch. 7 - The propagation speed of small-amplitude surface...
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
- Figure shows the flow of water over a dam. Thevolume fl ow Q is known to depend only on crest width B ,acceleration of gravity g , and upstream water height Habove the dam crest. It is further known that Q is proportionalto B . What is the form of the only possible dimensionallyhomogeneous relation for this flow rate?arrow_forwardWhen a fluid flows slowly past a vertical plate of height h and width b, pressure develops on the face of the plate. Assume that the pressure, p, at the midpoint of the plate is a function of plate height and width, the approach velocity V, and the fluid viscosity u and fluid density p. Make use of dimensional analysis to determine how the pressure, p will be formed with a dimensionless group. (Take b, V. p as repeating variables). Select one: O a. n1 = p /V² p O b. n1 = p/Ve O c.n1 = p/Vp? O d. 11 = p/V² p²arrow_forwardThe slope of the height h of a surface wave moving in a shallow pool of liquid is related to the speed of the wave u and gravity g by the following equation и ди дх g əx (a) Use a length scale L and a velocity scale Vo to 'nondimensionalize' the equation (b) What is the nondimensional parameter of the flow?arrow_forward
- Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?arrow_forwardThe Reynolds transport theorem (RTT) is discussed in Chap. 4 of your textbook. For the general case of a moving and/or deforming control volume, we write the RTT as follows: d pb dV + pbV-ñ dA dt dt dB sys where Vr is the relative velocity, i.e., the velocity of the fluid relative to the control surface. Write the primary dimensions of each additive term in the equation and verify that the equation is dimensionally homogeneous. Show all your work. (Hint: Since B can be any property of the flow-scalar, vector, or even tensor—it can have a variety of dimensions. So, just let the dimensions of B be those of B itself, {B}. Also, b is defined as B per unit mass.)arrow_forwardThe flow rate in a rectangular open channel can be measured by placing a plate along the channel as seen in the figure. This type of artifact is called "weir".The height of the water, H, above the ridge is referred to as "head" and can be used to determine the flow through the channel. Assume that flow Q is a function of H, channel width, b, and gravity, g.Determine a correct array of dimensionless variables for this problem.arrow_forward
- The Archimedes number, Ar, used in the flow of stratifiedfluids, is a dimensionless combination of gravity g , densitydifference Δ ρ , fluid width L , and viscosity μ . Find theform of this number if it is proportional to g .arrow_forwardQ1: If an air stream flowing at velocity (U) pasta body of length (L) causes a drag force (F) on the body which depends only upon U, L, and fluid viscosity μ. Formulate the suitable dimensionless parameter of the air drag force.arrow_forwardIn an experimental investigation, it is found that the discharge of oil through a pipeline relates to the pressure drop per unit length of the pipeline P, the radius of the pipe r, the density of oil p, the tapering angle 0 and the viscosity of oil µ. Derive the non-dimensional parameters related to this problem (you may use Buckingham's PI theorem)arrow_forward
- 3. The radius R of a mushroom cloud generated by a nuclear bomb grows in time. We expect that R is a function of time t, initial energy of the explosion E, and average air density p. Use dimensional analysis to express the relationship between R, t, E, and p in dimensionless form.arrow_forwardFluid Mechanics. Picture Attached.arrow_forwardIf you disturb a tank of length L and water depth h , thesurface will oscillate back and forth at frequency Ω ,assumed here to depend also upon water density ρ and theacceleration of gravity g . ( a ) Rewrite this as a dimensionlessfunction. ( b ) If a tank of water sloshes at 2.0 Hz onearth, how fast would it oscillate on Mars ( g ≈ 3.7 m/s 2 )?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 PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering 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
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY