Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.4P
Consider a velocity field where the x and y components of velocity are given by
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Consider
the velocity field represented by
V = K (yĩ + xk)
Rotation about z-axis is
velocity field is given by:
A two-dimensional
V = (x - 2y) i- (2x + y)Ĵj
a. Show that the flow is incompressible and irrotational.
b. Derive the expression for the velocity potential, (x,y).
c. Derive the expression for the stream function, 4(x,y).
An unsteady velocity field V=xy^2 ti+zxj-t^3 k exists at the 3D plane along a streamline that passes through the point (3,-1,2) at t=0. Find the equation representing this streamline.
Chapter 2 Solutions
Fundamentals of Aerodynamics
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...
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- Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). Calculate the equation of the streamline passing through the point (0, 5).arrow_forwardAn unsteady velocity field V = xy^2ti + zxj −t^3k exists at the 3D plane along a streamline that passes through the point (3,-1,2) at t = 0. Find the equation representing this streamline.arrow_forward1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.arrow_forward
- An unsteady velocity field V = xy'ti + zxj – t°k exists at the 3D plane along a streamline that passes through the point (3,-1,2) at t = 0. Find the equation representing this streamline.arrow_forwardIn three-dimensional fluid flow, the velocity component an u = * + y z, v = - (xy + yz + zx). Determine the %3D satisfy the continuity equation.arrow_forwardAt t = 0, an unstable velocity field V = xy²ti + zxj – t³k, emerges in the 3D plane as a result of a streamline passing through the points (3, -1, 2). Determine the equation that can act for the streamline.arrow_forward
- Consider a velocity field where the x and y components of velocity aregiven by u = cx and v = −cy, where c is a constant. Assuming the velocity field given is pertains to an incompressible flow, calculate the stream function and velocity potential.Using your results, show that lines of constant φ are perpendicular to linesof constant ψ.arrow_forwardConsider a velocity field where the x and y components of velocity are given by u = cx and v = -cy, where c is a constant. Obtain the equations of the streamlines.arrow_forwardAnswer question 3 in the attached image pleasearrow_forward
- need urgent help, thanks the question is related to advanced fluid mechanicsarrow_forwardA fluid has a velocity field defined by u = x + 2y and v = 4 -y. In the domain where x and y vary from -10 to 10, where is there a stagnation point? Units for u and v are in meters/second, and x and y are in meters. Ox = 2 m. y = 1 m x = 2 m, y = 0 No stagnation point exists x = -8 m, y = 4 m Ox = 1 m, y = -1 m QUESTION 6 A one-dimensional flow through a nozzle has a velocity field of u = 3x + 2. What is the acceleration of a fluid particle through the nozzle? Assume u, x and the acceleration are all in consistent units. O 3 du/dt 9x + 6 1.5 x2 + 2x O Oarrow_forward2. Consider the Eulerian velocity field u(x, t) = y i + (x – sin t) j, where x = x i + yj and t is the time. Please explain how to find an expression for the streamlines that pass through the point (0, yo) for yo ER. Then, find the nonparametric expression for the pathline of the particle that passes through the point (0, 1/2 ) at t = 0, describing the motion.arrow_forward
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