Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
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Chapter 5, Problem 49P
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a. Derive an equation for the material acceleration vector.b. Obtain the vorticity vector for the velocity field.c. Is the flow rotational or irrotational? Show through your derivation.d. Is the flow incompressible or compressible? Show through your derivation.
(3a)The first time derivative of vector A cross vector B is equal to the first time derivative of vector B cross vector A.
The first time derivative of vector A cross vector B is equal to the first time derivative of vector B cross vector A.
True
False
(b)
Suppose you're interested in the first time-derivative of velocity vector v(t) = (5t2)i + (2t)j. Which of the following expressions represents the first time-derivative of two times v(t)?
Suppose you're interested in the first time-derivative of velocity vector v(t) = (5t2)i + (2t)j. Which of the following expressions represents the first time-derivative of two times v(t)?
(10t)i + (2)j
(20t)i + (4)j
(10)i
(5/3)(t3)i + (t2)j
Flow through a converging nozzle can be approximated by a one-dimensional velocity
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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...
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- The velocity components of a flow field are given by: = 2x² – xy + z², v = x² – 4xy + y², w = 2xy – yz + y² (i) Prove that it is a case of possible steady incompressible fluid flow (ii) Calculate the velocity and acceleration at the point (2,1,3)arrow_forward1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.arrow_forwardQ: A flow field is given by: V = (x'y)i+(y°z)j–-(2x*yz+ yz*)k Prove that it is a case of possible steady incompressible fluid flow. Calculate the velocity and acceleration at the point (3,2.4).arrow_forward
- Please find the question attached. I don’t understand how to integrate when finding the pathline.arrow_forwardQ.5 The velocity components in x and y direction 2 are given by u = Axy° - xy; v = > ху; v — ху = xy² – 3/4 .4 y*. The value of A for a possible flow field involving an incompressible fluid is: A -3/4 В 3 C 4/3 D -4/3arrow_forwardIn Cartesian coordinates, a particular velocity field is defined by V = −2x2i + 4xyj + 3k. (a) Is this flow field compressible or incompressible? (b) Find the acceleration of the fluid at the point (1,3,0) (c) Find the volume flux passing through area A shown in Figure P5.16. (d) What are the dimensions of volume flux?arrow_forward
- Please solve it quicklyarrow_forward55. Derive the relation for angular velocity in terms of the velocity components for fluid rotation in a two-dimensional flow field. [Hint: Use the schematic for ro- tation in Figure IIa.3.5 and find the angular velocity for line oa as @a = doddt. Substitute for da= dl,/dx and for dl, from dl, = (JV,/dx)dxdt. Do the same for line ob to find @p. The z-component of rotation vector is the average of @a and @p. Do the same for x- and y- components].arrow_forwardPlease 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_forward
- Can I have a detailed explanation on filling the blanks in the following images? Thank you!arrow_forward6)arrow_forward3.4 Consider a steady, incompressible, 2D velocity field for motion parallel to the X-axis with constant shear. The shear rate is du/dy Ay. Obtain an expression for the velocity field V. Calculate the rate of rotation. Evaluate the stream function %3D for this flow field. Ay Ay + В і, о, Ay + By+ C 6. Ans: V= 2arrow_forward
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