Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 4, Problem 110P
To determine
The location of the stagnation point in the flow field.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
y
x = r cos 0
V = Or
y = r sine
r = √x² + y²
χ
Flow in "solid body rotation" acts like a solid spinning around an axis. The streamlines are circular,
the velocity is purely tangential, and the velocity magnitude is V = r, where is the angular
velocity (positive counter-clockwise) and r is the radius.
(a) Express the velocity vector V as a function of x and y.
(b) Calculate the curl of the velocity vector V × V, indicating clearly the direction of the resulting
vector.
1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par-
allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and
the width of each plate are L and W, respectively. The velocity distribution under steady
conditions is given by
JAP|B²
Vz =
2µL
B
a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution
takes the form
JAP|B?
v, =
2μL
Problems
11
- 2B --– €.
(a)
2B
(b)
Figure 1.3. Flow between parallel plates.
b) Calculate the volumetric flow rate by using the velocity distributions given above. What
is your conclusion?
2|A P|B³W
Answer: b) For both cases Q =
3µL
The three components are as follows:u = 2xt– 3xyz + 6zv = x– yz + 4xytw = 3x– 5yzt + yzFind the velocity and acceleration of a fluid particle at (1, 0, 1) at time, t = 0.
Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
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
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
- Velocity of a gas When a hot gas exits a cylindrical smoke- stack, its velocity varies throughout a circular cross section of the smokestack, with the gas near the center of the cross section having a greater velocity than the gas near the perime- ter. This phenomenon can be described by the formula V = Vmas where Vmax is the maximum velocity of the gas, ro is the radius of the smokestack, and V is the velocity of the gas at a distance r from the center of the circular cross section. Solve this formula for r.arrow_forward3.1. The velocity at a point in a fluid for a one-dimensional flow may be given in the Eulerian coordinates by u == AxBt. Show that x = f(x, t) in the Lagrange coordinates can be obtained from the Eulerian system. The in- itial position of the fluid particle is designated by x) and the initial time to = 0 may be assumed.arrow_forwardThe three components are as follows:u = 2xt– 3xyz + 6zv = x– yz + 4xytw = 3x– 5yzt + yzFind the velocity and acceleration of a fluid particle at (1, 0, 1) at time, t = N.arrow_forward
- Dynamics Under rectilinear motion the behavior of velocity is given by v=1+x^2 , where v is in ft/s and x is in ft. When x = 0, t = 0. a. Determine a relation a vs x b. Determine a relation t vs x c. Calculate the acceleration when x = 2 d. Calculate the velocity and acceleration when t = 4.arrow_forwardThe velocity component in the y-direction is given as v = 3x - 4y for the steady, inviscid and two- dimensional flow of an incompressible fluid. The only body force is the gravity, g, and it acts in the negative y-direction. The density of the fluid is p. For an irrotational flow, determine a) The velocity component in the x-direction, if it is zero at the origin b) The acceleration vector: ) and c) The pressure field, if the pressure is Po at the origin d) The stream function(arrow_forwardSparky needs to design a device that accelerates air in order to keep some the inflatable eagle fully inflated for some university events. The velocity through the device (V) is linear (ax + b, where a and b are constants). Since the inflatable is used on top of the ski/tubing run at Snowflex the wind velocity entering the device at x1 of 0 (V1) is 10 m/sec. Sparky needs the velocity at the exit of the 1 m-long (x2) device to be 25 m/sec (V2). For force calculations Sparky needs to know the local acceleration, convective acceleration, and total acceleration at the device inlet (x1 = 0 m) and exit (x2 = 1 m). What are these values?arrow_forward
- 5. A web page designer creates an animation in which a dot on a computer screen has position F = [4.0 cm + (2.5 cm/s²)ti + (5.0 cm/s)tj. (a) Find the magnitude and direction of the dot's average velocity between t = 0 and t = 2.0 S.arrow_forwardIf you are not sure pass it. I dont want wrong answers, hand written solution is also fine but wrong answer i will report. A body of mass 5 kg is projected vertically upward with an initial velocity 17 meters per second. The gravitational constant is 9.8 m/s2. The air resistance is equal to k|v| where k is a constant. (1)Find a formula for the velocity at any time v(t) in terms of k. (2)Find the limit of this velocity for a fixed time (t0) as the air resistance coefficient k goes to zero.arrow_forwardGiven the Eulerian velocity vector field: V = 3ti + xzj + ty²k Find the total acceleration of a particle av av av W дх' ду' ду Hint: u Varrow_forward
- 1) Particle Motion and Coordinate Systems y y = 0.001x² %3D 100 m The jet pictured above is following the given curve. All of the question below are related to the moment pictured a) If the jet's altitude is increasing at a rate of 40 m/s, find its velocity vector (in Cartesian) b) Find the speed of the jet c) In addition, if the rate of change of the jet's vertical speed is increasing at 15 m/,2, find the acceleration vector d) Find the tangential component of the acceleration vector, v e) Find the normal component of the acceleration vector f) Find the radius of curvature of the jet's path using the information from parts b) and e)arrow_forwardThe equations describing the position of a water stream (with respect to time) coming out of the hose, shown in the following figure, are given by the following. y X (Vy)o = 1.5 m/s Hose -Xo = 2m x = x₁ + (Vx) ot y = Y₁ + (V₂) ot — — — gt² 2 V (V₂) = 2.6 m/s Yo = 1.5 m In these relationships, x and y are position coordinates, x and y are initial coordinates of the tip of the hose, (Vx) and (V₂) are the initial velocities of water coming out of the hose in the x- and y-directions, g = 9.81 m/s², and t is time. Plot the x- and y-positions of the water stream as a function of time. Also, plot the path the water stream will follow as a function of time. Compute and plot the components of velocity of the water stream as a function of time. (Submit a file with a maximum size of 1 MB.)arrow_forward5. Find the rate at which a fluid flowing with constant velocity u (3,0,-1) crosses each of the following triangles: (а) [(-2, 1, 0), (5, 3, -1), (8, -5, 2)], (b) [(8, -5, 2), (5, 3,-1), (-2, 1,0)), (c) [(1,-1,0), (2, 0, 2), (3, –2, –3)), (d) [(0,0,0), (0, 1,0), (1,0,0)], (e) [(1,0,0), (0, 1,0), (0,0, 1)], (f) [(0,0,0), (0,0, 1), (0, 1, 0)), (g) [(0,0,0), (1,0, 0), (0,0, 1)].arrow_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
Physics 33 - Fluid Statics (1 of 10) Pressure in a Fluid; Author: Michel van Biezen;https://www.youtube.com/watch?v=mzjlAla3H1Q;License: Standard YouTube License, CC-BY