FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 4, Problem 60P
To determine
The x and y component of acceleration field.
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An Eulerian velocity vector field is described by V = i + 2zj − 3x2k, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (i) Is the flow incompressible or compressible? (ii) Find the rate of change of velocity following a fluid particle. (iii) Find the viscous force per unit volume (that is, the viscous term in the Navier-Stokes equation).
4. A steady, incompressible, and two-dimensional velocity field is given by the following
components in the xy-plane:
Vxu = 2.65 + 3.12x + 5.46y
=
Vy=
=v=0.8+ 5.89x² + 1.48y
=
Calculate the acceleration field (find expressions for acceleration components ax and ay and
calculate the acceleration at the point (x,y) = (-1,3).
4. Consider a velocity field V = K(yi + ak) where K is a constant. The vorticity, z , is
(A) -K
(B) K
(C) -K/2
(D) K/2
Chapter 4 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
Ch. 4 - What does the word kinematics mean? Explain what...Ch. 4 - Briefly discuss the difference between derivative...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - -5 A steady, two-dimensional velocity field is...Ch. 4 - Consider steady flow of water through an...Ch. 4 - What is the Eulerian description of fluid motion?...Ch. 4 - Is the Lagrangian method of fluid flow analysis...Ch. 4 - A stationary probe is placed in a fluid flow and...Ch. 4 - A tiny neutrally buoyant electronic pressure probe...
Ch. 4 - Define a steady flow field in the Eulerian...Ch. 4 - Is the Eulerian method of fluid flow analysis more...Ch. 4 - A weather balloon is hunched into the atmosphere...Ch. 4 - A Pilot-stalk probe can often be seen protruding...Ch. 4 - List at least three oiler names for the material...Ch. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - For the velocity field of Prob. 4-6, calculate the...Ch. 4 - Consider steady flow of air through the diffuser...Ch. 4 - For the velocity field of Prob. 4-21, calculate...Ch. 4 - A steady, incompressible, two-dimensional (in the...Ch. 4 - The velocity field for a flow is given by...Ch. 4 - Prob. 25CPCh. 4 - What is the definition of a timeline? How can...Ch. 4 - What is the definition of a streamline? What do...Ch. 4 - Prob. 28CPCh. 4 - Consider the visualization of flow over a 15°...Ch. 4 - Consider the visualization of ground vortex flow...Ch. 4 - Consider the visualization of flow over a sphere...Ch. 4 - Prob. 32CPCh. 4 - Consider a cross-sectional slice through an array...Ch. 4 - A bird is flying in a room with a velocity field...Ch. 4 - Conversing duct flow is modeled by the steady,...Ch. 4 - The velocity field of a flow is described by...Ch. 4 - Consider the following steady, incompressible,...Ch. 4 - Consider the steady, incompressible,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - The velocity field for a line some in the r plane...Ch. 4 - A very small circular cylinder of radius Rtis...Ch. 4 - Consider the same two concentric cylinders of...Ch. 4 - The velocity held for a line vartex in the r...Ch. 4 - Prob. 47PCh. 4 - Name and briefly describe the four fundamental...Ch. 4 - Prob. 49CPCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Using the results of Prob. 4—57 and the...Ch. 4 - Converging duct flow (Fig. P4—16) is modeled by...Ch. 4 - Prob. 60PCh. 4 - For the velocity field of Prob. 4—60, what...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Prob. 67PCh. 4 - Consider the steady, incompressible,...Ch. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - A cylindrical lank of water rotates in solid-body...Ch. 4 - Prob. 75PCh. 4 - A cylindrical tank of radius rrim= 0.354 m rotates...Ch. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - For the Couette flow of Fig. P4—79, calculate the...Ch. 4 - Combine your results from Prob. 4—80 to form the...Ch. 4 - Consider a steady, two-dimensional, incompressible...Ch. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Consider the following steady, three-dimensional...Ch. 4 - Prob. 85PCh. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Briefly explain the purpose of the Reynolds...Ch. 4 - Prob. 88CPCh. 4 - True or false: For each statement, choose whether...Ch. 4 - Consider the integral ddtt2tx2. Solve it two ways:...Ch. 4 - Prob. 91PCh. 4 - Consider the general form of the Reynolds...Ch. 4 - Consider the general form of the Reynolds...Ch. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - The velocity field for an incompressible flow is...Ch. 4 - Consider fully developed two-dimensional...Ch. 4 - For the two-dimensional Poiseuille flow of Prob....Ch. 4 - Combine your results from Prob. 4—100 to form the...Ch. 4 - Prob. 103PCh. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 116PCh. 4 - Based on your results of Prob. 4—116, discuss the...Ch. 4 - Prob. 118PCh. 4 - In a steady, two-dimensional flow field in the...Ch. 4 - A steady, two-dimensional velocity field in the...Ch. 4 - A velocity field is given by u=5y2,v=3x,w=0 . (Do...Ch. 4 - The actual path traveled by an individual fluid...Ch. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Water is flowing in a 3-cm-diameter garden hose at...Ch. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - Prob. 129PCh. 4 - Prob. 130PCh. 4 - Prob. 131PCh. 4 - An array of arrows indicating the magnitude and...Ch. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Prob. 135PCh. 4 - A steady, two-dimensional velocity field is given...Ch. 4 - Prob. 137PCh. 4 - Prob. 138PCh. 4 - Prob. 139PCh. 4 - Prob. 140PCh. 4 - Prob. 141P
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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
- 2. Consider the two-dimensional time-dependent velocity field u(x, t) = (sint, cost, 0), in the basis of Cartesian coordinates. a) Determine the streamlines passing through the point x = 0 at the times t = 0, π/2, π and 3π/2. b) Determine the paths of fluid particles passing through the point x = 0 at the same times, to = 0, π/2, 7 and 37/2. Hence, describe their motion. ㅠ c) Find the streakline produced by tracer particles continuously released at the point xo = 0 and find its position at t = 0, π/2, π and 37/2. Hence describe its motion.arrow_forwardConsider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis isarrow_forwardfluid mechanicsarrow_forward
- A incompressible, steady, velocity field is given by the following components in the x-y plane: u = 0.205 + 0.97x + 0.851y ; v = v0 + 0.5953x - 0.97y How would I calculated the acceleration field (ax and ay), and the acceleration at the point, v0= -1.050 ? Any help would be greatly appreciated :)arrow_forwardAn Eulerian velocity vector field is described by V = 2x2yi − 2xy2j − 4xyk, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is the flow one-, two- or three-dimensional? (b) Is the flow compressible or incompressible? (c) What is the x-component of the acceleration following a fluid particle? (d) Bonus question: Is the flow irrotational?arrow_forwardA velocity field (V) is specified as: V =5x²î +6zî + 4x²tk (units of velocity in [m/s]) Calculate z-component of the convective acceleration at (1,1,1) and t=1.arrow_forward
- in the X-Y plane; permanent, 2B, in an uncompressed flow, a, b and C are constant there is a velocity field defined as follows. a-) Continuity equation show that it is provided. b-) calculate the pressure as a function of x and y?arrow_forwardConsider the following steady, two-dimensional, incompressible velocity field: V = (u,v) = (3ax²)i + (3axy)j Where a is a constant. Calculate the mechanical pressure (Pm) as a function of the static pressure (P), X, y, and viscosity (µ).arrow_forwardprovide explanation and free body diagram for each part also commentarrow_forward
- a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.arrow_forwardQuestion 3 (a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y > 0 is defined as: v = -Upxy i+ Upxy j where i and j are the unit vectors in the x- and y-directions respectively and Uo is a constant with units m/s. (i) Determine the magnitude and direction of the velocity at the point (1,1). (ii) Find the equation of the streamlines.arrow_forwardPlease answer with detailarrow_forward
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