FUND OF AERODYNAMICS(LLF) +CONNECT (1YR)
6th Edition
ISBN: 9781265141387
Author: Anderson
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2, Problem 2.10P
Consider a flow field in polar coordinates, where the stream function is given as
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1. Consider a three-dimensional steady incompressible flow with components:
u =-x(y+z), v= y, w=÷(z²-2yz),
(a) Is the flow locally rotating? Justify your answer.
(b) Determine the equation of vortex lines.
(c) Are the vortex lines perpendicular to the streamlines?
1. For incompressible flows, their velocity field
2. In the case of axisymmetric 2D incompressible flows,
where is Stokes' stream function, and
u = VXS,
S(r, z, t) =
Uz =
where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence
1 Ꭷ
r dr
1 dy
r dz
Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads
Y(R, 0, t)
R sin 0
S(R, 0, t)
UR
uo
Y(r, z, t)
r
=
=
-eq,
and
Up = =
1
ay
R2 sin Ꮎ ᎧᎾ
1 ƏY
R sin Ꮎ ᎧR
-eq
2
(1)
(2)
(3)
An incompressible stream function is given byψ = aθ +br sin θ. ( a ) Does this flow have a velocitypotential? ( b ) If so, find it.
Chapter 2 Solutions
FUND OF AERODYNAMICS(LLF) +CONNECT (1YR)
Ch. 2 - Consider a body of arbitrary shape. If the...Ch. 2 - Consider an airfoil in a wind tunnel (i.e., a wing...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the radial and...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - The velocity field given in Problem 2.3 is called...Ch. 2 - The velocity field given in Problem 2.4 is called...Ch. 2 - Is the flow field given in Problem 2.5...Ch. 2 - Consider a flow field in polar coordinates, where...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
The triple jump is a track-and-field event in which an athlete gets a running start and tries to leap as far as...
Vector Mechanics For Engineers
Locate the centroid of the area. Prob. 9-17
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
A biological fluid moves at a flow rate of m=0.02kg/s through a coiled, thin-walled, 5-mm-diameter tube submerg...
Fundamentals of Heat and Mass Transfer
What is the importance of modeling in engineering? How are the mathematical models for engineering processes pr...
Heat and Mass Transfer: Fundamentals and Applications
Select a mechanical component from Part 3 of this book (roller bearings, springs, etc.), go to the Internet, an...
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Comprehension Check 7-14
The power absorbed by a resistor can be given by P = I2R, where P is power in units of...
Thinking Like an Engineer: An Active Learning Approach (3rd 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
- An Eulerian velocity vector field is described by V = 2i + yz2tj −z3t3k, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is the flow incompressible or compressible? (d) Find the z-component of the acceleration vector.arrow_forward2. Consider a stream function given by = (²+x²). (a) Does this flow satisfy conservation of mass? Show your work. (b) Plot the streamlines for this flow. Let K= 2. Be sure to indicate the direction of the flow. (c) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that a velocity potential does not exist. (d) Describe the flow represented by this stream function.arrow_forward(b) Two velocity components of a steady, incompressible flow field are given as follows; u = 2ax + bxy + cy? v = axz – byz? where a, b and c are constants. Determine an expression for w as a function of x, y, and z.arrow_forward
- Problem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.arrow_forwardAsaparrow_forward(a) A two-dimensional flow field is given byu = 5x 2 − 5y 2v = −10xy(i) Find the streamfunction ψ and velocity potential φ.(ii) Find the equation for the streamline and potential line which passesthrough the point (1, 1).arrow_forward
- The velocity of flow of fluid is represented by the equation: V=2xi +3vj. The equation of the stream line passing through the point (4,3) is (A) 0.72x = 1,2 (B)¹ = 0.72x¹/² (C) 0.72x2=2 (D) None of thesearrow_forward6. Find the stream function associated with the two-dimensional incompressible, possible flow with velocity components given by a2 Ur = b|1- cos e and ug = -b1+- sin 0 r2 Where a, and b are known constants.arrow_forward(a) A two-dimensional flow field is given by u = 5a2 – 5y, v = -10xy (i) Find the streamfunction and velocity potential Ø. (ii) Find the equation for the streamline and potential line which passes through the point (1, 1).arrow_forward
- For a certain two-dimensional incompressible flow, velocity field is given by 2xy î - yj. The streamlines for this flow are given by the family of curvesarrow_forward3.3 Starting with a small fluid element of volume dx dy dz, derive the continuity equation (Eq. 3.4) in rectangular cartesian coordinates.arrow_forward3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric = equation for the pathline of the particle that passed through (1.1) at t = 0. (ii) Without calculating any equation: if I were to draw the streak-line at t = 0 of all points that passed through (1, 1) would it be the same or different? Justify yourself.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
Introduction to Kinematics; Author: LearnChemE;https://www.youtube.com/watch?v=bV0XPz-mg2s;License: Standard youtube license