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
Videos
Textbook Question
Chapter 5, Problem 70P
A linear velocity profile was used to model flow in a laminar incompressible boundary layer in Problem 5.10. Express the rotation of a fluid particle. Locate the maximum rate of rotation. Express the rate of angular deformation for a fluid particle. Locate the maximum rate of angular deformation. Express the rates of linear deformation for a fluid particle. Locate the maximum rates of linear deformation. Express the shear force per unit volume in the x direction. Locate the maximum shear force per unit volume; interpret this result.
5.10 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
Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively.
The lift on a spinning circular cylinder in a freestream with a velocity of30 m/s and at standard sea level conditions is 6 N/m of span. Calculate thecirculation around the cylinder.
A flow is non-uniform when the magnitude of the parameters varies from point to point along the flow path.
TRUE
FALSE
Using the irrotational flow approximation, calculate and plot the nondimensional static pressure distribution on the surface of a circular cylinder of radius a in a uniform stream of speed V∞. Discuss the results. The pressure far away from the cylinder is P∞.
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...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
Neglect the size of the corner welds at A and B for the calculation. Prob. 9-58
Engineering Mechanics: Statics
What parts are included in the vehicle chassis?
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Determine the resultant internal loadings acting on the cross sections at points D and E of the frame.
Mechanics of Materials (10th Edition)
The force in each supporting cable.
Engineering Mechanics: Statics & Dynamics (14th Edition)
State if the members are in tension or compression. Prob. F6-8
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Comprehension Check 8-1
The engine on a spacecraft nearing Mars can provide a thrust of 15,000 newtons [N]. If ...
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
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
- Consider steady, incompressible, parallel, laminar flow of a film of oil falling slowly down an infinite vertical wall. The oil film thickness is h, and gravity acts in the negative z-direction. There is no applied (forced) pressure driving the flow—the oil falls by gravity alone., except for the case in which the wall is inclined at angle ?. Generate expressions for both the pressure and velocity fields. As a check, make sure that your result agrees with that of when ? = 90°. [Hint: It is most convenient to use the (s, y, n) coordinate system with velocity components (us, ?, un), where y is into the page in Fig. Plot the dimensionless velocity profile us* versus n* for the case in which ? = 60°.]arrow_forwardThis is a practice question, not graded assignment. Understand that to find the answer to below question, we need to solve Navier-Stokes and energy equation for this flow to derive the velocity profile and temperature profile. Please show step-by-step equations including step-by-step integration. Please also provide explanation. An incompressible fluid flows through a rectangular cross section duct, with width much larger than height of the cross section. The duct surface is heated at a uniform rate along its length. If the centreline of the flow is along the centre of the duct where y = 0, the distance from the centreline to the surface of the duct is b = 25 mm, and the thermal conductivity of the fluid is 0.6 W/mK, what is the local heat transfer coefficient in the developed region of the flow? Give your answer in W/m^2K to 1 decimal place.arrow_forwardA sink of strength 20 m2/s is situated 3 m upstream of a source of 40 m²/s in a uniform stream. It is found that, at a point 2.5 m from both source and sink, the local velocity is normal to the line joining the source and sink. Find the velocity at this point and the velocity of the uniform stream. Locate any stagnation points and sketch the flow field.arrow_forward
- Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction (into the page in Fig. There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. Calculate the velocity and pressure fields, and estimate the shear force per unit area acting on the bottom plate.arrow_forwardIn two dimensions along the converging nozzle, stable, considering incompressible flow. The velocity on the horizontal centerline (x-axis) is given as V=V1(1+x/L)i Derive an equation for the acceleration of a particle moving along the centerline using (a) Euler's approximation and (b) Lagrangian approximation. Discuss the acceleration for the particle being at the beginning and end of the channel.arrow_forwardEvaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK, hc=102W/m2K.arrow_forward
- Please indicate the given, assumption and illustration. A source with strength 0.25 m2/s and a vortex with strength 1 m2/s (counter-clockwise) are located at the origin. After working out the equations for the stream function and velocity potential components, determine the following velocity components at a point P(1, 0.5): A) The Radial Velocity component in meters/second. B) The Tangential Velocity Component in meters/second.arrow_forwardOutside an inner, intense-activity circle of radius R , a tropicalstorm can be simulated by a polar-coordinate velocitypotential ϕ ( r , θ ) = U o R θ , where U o is the wind velocity atradius R . ( a ) Determine the velocity components outsider = R . ( b ) If, at R = 25 mi, the velocity is 100 mi/h and thepressure 99 kPa, calculate the velocity and pressure atr =100 mi.arrow_forwardThe purpose of this problem is to give you a feel for the magnitude ofReynolds number appropriate to real airplanes in actual flight. a. Consider the DC-3 shown in (1.1). The wing root chord length(distance from the front to the back of the wing where the wing joinsthe fuselage) is 14.25 ft. Consider the DC-3 flying at 200 miles perhour at sea level. Calculate the Reynolds number for the flow over thewing root chord. (This is an important number, because as we will seelater, it governs the skin-friction drag over that portion of the wing.)b. Consider the F-22 shown in (1.5), and also gracing the cover ofthis book. The chord length where the wing joins the center body is21.5 ft. Consider the airplane making a high-speed pass at a velocityof 1320 ft/s at sea level (Mach 1.2). Calculate the Reynolds number atthe wing root.arrow_forward
- The wing of the Fairchild Republic A-10A twin-jet close-support airplane is approximately rectangular with a wingspan (the length perpendicular to the flow direction) of 17.5 m and a chord (the length parallel to the flow direction) of 3 m. The airplane is flying at standard sea level with a velocity of 200 m/s. Assume the wing is approximated by a flat plate and incompressible flow. If the critical Reynolds number for transition is 106, calculate the skin friction drag for the wing. Use turbulent drag as 2830 N. (Round the final answer to the nearest whole number.)arrow_forwardWater falls down a vertical pipe by gravity alone. The flow between vertical locations z1 and z2 is fully developed, and velocity profiles at these two locations are sketched. Since there is no forced pressure gradient, pressure P is constant everywhere in the flow (P = Patm). Calculate the modified pressure at locations z1 and z2. Sketch profiles of modified pressure at locations z1 and z2. Discuss.arrow_forwardA particle of 2 mm in diameter and density of 2500 kg/m3 issettling in a stagnant fluid in the Stokes’ flow regime.a) Calculate the viscosity of the fluid if the fluid density is 1000kg/m3 and the particle falls at a terminal velocity of 4 mm/s.b) What is the drag force on the particle at these conditions?c) What is the particle drag coefficient at these conditions?d) What is the particle acceleration at these conditions?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License