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 15P
The boundary-layer thickness, δ, on a smooth flat plate in an incompressible flow without pressure gradients depends on the free-stream speed, U, the fluid density, ρ, the fluid viscosity, μ, and the distance from the leading edge of the plate, x. Express these variables in dimensionless form.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
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?
Q1: 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.
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)
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...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
How does the laser produce coherent light (stimulated emission)?
Degarmo's Materials And Processes In Manufacturing
Big data Big data describes datasets with huge volumes that are beyond the ability of typical database manageme...
Management Information Systems: Managing The Digital Firm (16th Edition)
Create a flowchart that shows the necessary steps for making the cookies in the following recipe: Ingredients: ...
Starting Out With Visual Basic (8th Edition)
Alphabetic Telephone Number Translator Many companies use telephone numbers like 555-GET-FOOD so the number is ...
Starting Out with Python (4th Edition)
Show a snippet of PHP code for creating a recordset. Explain the meaning of the code.
Database Concepts (8th Edition)
Explain why SQL is called a set-oriented language.
Modern Database Management
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
- 3- Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if necessary to agree with the standard dimensionless groups in fluid mechanics.arrow_forwardThe drag FD of the golf ball is affected by the speed V of the ball, the diameter d of the ball, the depth , of the dimple, the radius r of the dimple, the density C of the dimple, the density of air, and the viscosity µ. Perform a dimensional analysis to represent the drag of the golf ball as a function of these variables.arrow_forwardTaylor number (Ta) is used here to describe the ratio between the inertia effect and the viscous effect. By applying Buckingham Pi's Theorem, determine an equation for Ta as a function of the radius of inner cylinder (r), cylinder tangential velocity (v), fluid dynamic viscosity (u), gap distance (L) and fluid density (p). Q4arrow_forward
- The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five variables: accelerationof gravity g , viscosity μ , density ρ , particle velocity U ,and particle diameter D . ( a ) If St is proportional to μand inversely proportional to g , find its form . ( b ) Showthat St is actually the quotient of two more traditionaldimensionless groups.arrow_forwardThe power P generated by a certain windmill design dependson its diameter D , the air density ρ , the wind velocity V , therotation rate Ω , and the number of blades n . ( a ) Write this relationship in dimensionless form. A model windmill, of diameter50 cm, develops 2.7 kW at sea level when V = 40 m/s andwhen rotating at 4800 r/min. ( b ) What power will be developedby a geometrically and dynamically similar prototype, ofdiameter 5 m, in winds of 12 m/s at 2000 m standard altitude?( c ) What is the appropriate rotation rate of the prototype?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_forward
- When a steady uniform stream flows over a circular cylinder, vortices are shed at a periodic rate. These are referred to as Kármán vortices. The frequency of vortex shedding få is defined by the free-stream speed V, fluid density p, fluid viscosity u, and cylinder diameter D. Use the Buckingham Pi method to show a dimensionless relationship for Kármán vortex shedding frequency is St = f (Re). Show all your work. V Darrow_forward1ODiem # 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. Farrow_forwardA boundary layer is a thin region (usually along a wall) in which viscous forces are significant and within which the flow is rotational. Consider a boundary layer growing along a thin flat plate. The flow is steady. The boundary layer thickness ? at any downstream distance x is a function of x, free-stream velocity V∞, and fluid properties ? (density) and ? (viscosity). Use the method of repeating variables to generate a dimensionless relationship for ? as a function of the other parameters. Show all your work.arrow_forward
- A uniform stream overflows in a circular cylinder and then a periodic Kármán vortex street is created. Through repeating variables, how can I create a dimensionless relationship for Kármán vortex shedding frequency (fk), where free-stream speed is V, fluid density is p, fluid viscosity is μ, and cylinder's diameter is d?arrow_forwardMott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?arrow_forwardThe power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate Ohm, the density rho, and viscosity mu of the fluid. Rewrite this as a dimensionless relationshiparrow_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