Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.5P
Consider a velocity field where the radial and tangential components of velocity arc
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The components of a two-dimensional velocity field are u = 4 + y³ and v = 16.
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b. Derive the expression for the velocity potential, (x,y).
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Chapter 2 Solutions
Fundamentals of Aerodynamics
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- Consider 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_forwardIn a certain steady, two-dimensional flow field the fluid den- sity varies linearly with respect to the coordinate x; that is, p = Ax where A is a constant. If the x component of velocity u is given by the equation u = y, determine an expression for v.arrow_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
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- The stream function in a two-dimensional flow field is given by y=x²- y². Then the magnitude of velocity at point (1, 1) isarrow_forwardThe radial velocity component in a incomplreesible, two-dimensional steady flow field (v2=0) is in the figure. Determine the acceleration field a(->) (r,θ)arrow_forwardConsider the flow field V = (ay+dx)i + (bx-dy)j + ck, where a(t), b(t), c(t), and d(t) are time dependent coefficients. Prove the density is constant following a fluid particle, then find the pressure gradient vector gradP, Γ for a circular contour of radius R in the x-y plane (centered on the origin) using a contour integral, and Γ by evaluating the Stokes theorem surface integral on the hemisphere of radius R above the x-y plane bounded by the contour.arrow_forward
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