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
Videos
Textbook Question
Chapter 5, Problem 10P
A crude approximation for the x component of velocity in an incompressible laminar boundary layer is a linear variation from u = 0 at the surface (y = 0) to the freestream velocity, U, at the boundary-layer edge (y = δ). The equation for the profile is u = Uy/δ, where δ = cx1/2 and c is a constant. Show that the simplest expression for the y component of velocity is υ = uy/4x. Evaluate the maximum value of the ratio υ/U, at a location where x = 0.5 m and δ = 5 mm.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An equation for the velocity for a 2D planar converging nozzle is
Uy
u =U1+
w=0
L
Where U is the speed of the flow entering into the nozzle, and L is the length. Determine if these satisfy the continuity
equation. Write the Navier-Stokes equations in x and y directions, simplify them appropriately, and integrate to
determine the pressure distribution P(x.y) in the nozzle. Assume that at x = 0, y = 0, the pressure is a known value, P.
Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt.
a. If the velocity distribution for the laminar boundary layer over a flat plate is given by :-
** (²) ² -
21
+ A₂ x
U
A₁ + A₂ x
Determine the form of the velocity profile by using the necessary boundary conditions. After
that by using the Von-Karman integral momentum equation find an expression in terms of the
Reynolds number to evaluate 1- Boundary Layer Thickness
Force
2-Wall Shear Stress 3-Drag
5- Displacement Thickness
+ A₁ x
4- Local and Average Skin Friction Coefficients
6- Momentum Thickness 7- Energy Thickness
Chapter 5 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 5 - Which of the following sets of equations represent...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - In an incompressible three-dimensional flow field,...Ch. 5 - In a two-dimensional incompressible flow field,...Ch. 5 - The three components of velocity in a velocity...Ch. 5 - The x component of velocity in a steady,...Ch. 5 - The y component of velocity in a steady...Ch. 5 - The velocity components for an incompressible...Ch. 5 - The radial component of velocity in an...Ch. 5 - A crude approximation for the x component of...
Ch. 5 - A useful approximation for the x component of...Ch. 5 - A useful approximation for the x component of...Ch. 5 - For a flow in the xy plane, the x component of...Ch. 5 - Consider a water stream from a jet of an...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - For an incompressible flow in the r plane, the r...Ch. 5 - A viscous liquid is sheared between two parallel...Ch. 5 - A velocity field in cylindrical coordinates is...Ch. 5 - Determine the family of stream functions that...Ch. 5 - The stream function for a certain incompressible...Ch. 5 - Determine the stream functions for the following...Ch. 5 - Determine the stream function for the steady...Ch. 5 - Prob. 23PCh. 5 - A parabolic velocity profile was used to model...Ch. 5 - A flow field is characterized by the stream...Ch. 5 - A flow field is characterized by the stream...Ch. 5 - Prob. 27PCh. 5 - A flow field is characterized by the stream...Ch. 5 - In a parallel one-dimensional flow in the positive...Ch. 5 - Consider the flow field given by V=xy2i13y3j+xyk....Ch. 5 - Prob. 31PCh. 5 - The velocity field within a laminar boundary layer...Ch. 5 - A velocity field is given by V=10ti10t3j. Show...Ch. 5 - The y component of velocity in a two-dimensional,...Ch. 5 - A 4 m diameter tank is filled with water and then...Ch. 5 - An incompressible liquid with negligible viscosity...Ch. 5 - Sketch the following flow fields and derive...Ch. 5 - Consider the low-speed flow of air between...Ch. 5 - As part of a pollution study, a model...Ch. 5 - As an aircraft flies through a cold front, an...Ch. 5 - Wave flow of an incompressible fluid into a solid...Ch. 5 - A steady, two-dimensional velocity field is given...Ch. 5 - A velocity field is represented by the expression...Ch. 5 - A parabolic approximate velocity profile was used...Ch. 5 - A cubic approximate velocity profile was used in...Ch. 5 - The velocity field for steady inviscid flow from...Ch. 5 - Consider the incompressible flow of a fluid...Ch. 5 - Consider the one-dimensional, incompressible flow...Ch. 5 - Expand (V)V in cylindrical coordinates by direct...Ch. 5 - Determine the velocity potential for (a) a flow...Ch. 5 - Determine whether the following flow fields are...Ch. 5 - The velocity profile for steady flow between...Ch. 5 - Consider the velocity field for flow in a...Ch. 5 - Consider the two-dimensional flow field in which u...Ch. 5 - Consider a flow field represented by the stream...Ch. 5 - Fluid passes through the set of thin, closely...Ch. 5 - A two-dimensional flow field is characterized as u...Ch. 5 - A flow field is represented by the stream function...Ch. 5 - Consider the flow field represented by the stream...Ch. 5 - Consider the flow field represented by the stream...Ch. 5 - Consider the velocity field given by V=Ax2i+Bxyj,...Ch. 5 - Consider again the viscometric flow of Example...Ch. 5 - The velocity field near the core of a tornado can...Ch. 5 - A velocity field is given by V=2i4xjm/s. Determine...Ch. 5 - Consider the pressure-driven flow between...Ch. 5 - Consider a steady, laminar, fully developed,...Ch. 5 - Assume the liquid film in Example 5.9 is not...Ch. 5 - Consider a steady, laminar, fully developed...Ch. 5 - Consider a steady, laminar, fully developed...Ch. 5 - A linear velocity profile was used to model flow...Ch. 5 - A cylinder of radius ri rotates at a speed ...Ch. 5 - The velocity profile for fully developed laminar...Ch. 5 - Assume the liquid film in Example 5.9 is...Ch. 5 - The common thermal polymerase chain reaction (PCR)...Ch. 5 - A tank contains water (20C) at an initial depth y0...Ch. 5 - For a small spherical particle of styrofoam...Ch. 5 - Use Excel to generate the progression to an...
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 immiscible Newtonian liquids, A and B, are in steady laminar flow between two parallelplates. Which, if any, of the velocity profiles shown below are impossible? Explain your answerscarefully.shear stress is visocsity time dux/dyarrow_forwardTwo infinite plates a distance h apart are parallel to the xzplane with the upper plate moving at speed V, as inFig. There is a fluid of viscosity μ and constant pressurebetween the plates. Neglecting gravity and assumingincompressible turbulent flow u(y) between the plates, usethe logarithmic law and appropriate boundary conditions toderive a formula for dimensionless wall shear stress versusdimensionless plate velocity. Sketch a typical shape of theprofile u(y).arrow_forwardConsider a velocity field where the radial and tangential components ofvelocity are Vr = 0 and Vθ = cr, respectively, where c is a constant. Is the flow field given is irrotational? Prove your answer.arrow_forward
- Please just solve for question (b) i will be extremly appreciate!!!!!arrow_forward2. Consider laminar flat plate flow with the following approximate velocity profile: U[1-exp(-5y/6)] which satisfies the conditions u=0 at y=0 and u=0.993U at y = 8 a) Does this expression satisfy boundary condition applicable to the laminar boundary layer velocity profile? Determine b) the boundary-layer thickness variation (8/x) c) the displacement thickness variation (6*/x) d) the momentum thickness variation (0/x) e) the drag coefficient f) the drag force (FD) on the surface of the plate g) the shear stress on both sides of the plate h) Now explain why your results in parts (b) through (c) are deplorably inaccurate compared to the exact Blasius solution.arrow_forwardConsider a large dirigible (like the Goodyear blimp) with length L = 240 m, and average diameter D = 40 m moving at a speed U = 135 km/hr at high altitude where the air density is p = 0.9 kg/m³ and the dynamic viscosity is u = 1.8 x 10-5 N – s/m². Because of the large size of the blimp and its large radius of curvature the primary forces acting on it are due to shear stresses at the surface, and the entire surface area can be approximated by its layout as a flat plate. Determine the drag force acting on the dirigible due to shear stresses, and the power required for the engine.arrow_forward
- Please answer with detailarrow_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.arrow_forwardPlease solve the following fluid mechanics questionsarrow_forward
- The wing of a tactical support aircraft is approximately rectangular with a wingspan (the length perpendicular to the flow direction) of 16.5 m and a chord (the length parallel to the flow direction) of 2.75 m. The airplane is flying at standard sea level with a velocity of 250 ms¯¹. Assume the wing is approximated by a flat plate. Assume incompressible flow. Use μ = 1.789 x 10-5 kg/ms (a) If the flow is considered to be completely laminar, calculate the boundary layer thickness at the trailing edge and the total skin friction drag.arrow_forwardAn incompressible viscous flow is contained between two parallel plates separated from each other by distance b. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U = 9.5 m/s and b = 3.2 cm, and there is no pressure gradient in the flow direction. a) Start with Navier-Stokes equations and determine the velocity at the point x = 7 cm and y= 0.56 cm. b) Calculate the magnitude of the vorticity at the same point. c) Calculate the rate of angular deformation at the same point. Work to 4 significant digits. Enter all values using base units or their combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa. You can use values with exponents, such as 0.12e3.arrow_forwardA potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy . Determine the velocity in x-direction u=? and Stream Function SF=? ( x2 : square of x ; x3: third power of x ; y2: square of y , y3: third power of y)ANSWER: u= 3 x2 - 3 y2 SF= 3 x2 y - y3arrow_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
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY