Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 6, Problem 6.2P
Prove that three-dimensional source flow is a physically possible incompressible flow.
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Prove that three-dimensional source flow is a physically possibleincompressible flow.
Consider steady, incompressible, two-dimensional flow due to a line source at the origin. Fluid is created at the origin and spreads out radially in all directions in the xy-plane. The net volume flow rate of created fluid per unit width is V·/L (into the page of Fig), where L is the width of the line source into the page in Fig Since mass must be conserved everywhere except at the origin (a singular point), the volume flow rate per unit width through a circle of any radius r must also be V·/L. If we (arbitrarily) specify stream function ? to be zero along the positive x-axis (? = 0), what is the value of ? along the positive y-axis (? = 90°)? What is the value of ? along the negative x-axis (? = 180°)?
If a flow field is compressible, what can we say about the material derivative of density? What about if the flow field is incompressible?
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- Show that the velocity of an incompressible flow has zero divergence.arrow_forwardFor 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_forwardSteady, one-dimensional incompressible between two plates separated by a distance H is given by V = Ui y H Where U is the speed of the upper plate and the lower plate is at rest. (a) Is the fluid accelerating? (b) What is the force acting on the plates? (c) What is the angular velocity?arrow_forward
- If the vorticity in a region of the flow is zero, the flow is (a) Motionless (b) Incompressible (c) Compressible (d ) Irrotational (e) Rotationalarrow_forwardFind stream function and velocity potential.arrow_forwardQ1 (a) If a flow field is compressible, what can you say about the material derivative of density? What about if the flow field is incompressible? Justify your answer.arrow_forward
- A CFD model of steady two-dimensional incompressiblefl ow has printed out the values of stream function ψ ( x , y ), inm 2 /s, at each of the four corners of a small 10-cm-by-10-cmcell, as shown in Fig. P4.70. Use these numbers to estimate the resultant velocity in the center of the cell and its angleα with respect to the x axis.arrow_forwardConsider 3D flow with velocity components below. u=x²+2xy v=2x-y²+z² w=-2xz+y² Is this flow incompressible? Show your work. b. Is this flow irrotational? Show your work.arrow_forwardVelocity components u = (Axy³ – x²y), v = xy² . possible flow field involving steady incompressible flow is then value of 2 for (a) 0 (b) 1 (c) 2 (d) 3arrow_forward
- Outer pipe wall Consider the steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe annulus of inner radius R, and outer radius Ro. Assume that the pressure is constant everywhere there is no forced pressure gradient driving the flow, Pi = P2. However, let the inner cylinder be moving at steady velocity V to the right, essentially a piston. The outer cylinder is stationary. This makes an axisymmetric Couette flow. Use cylindrical coordinates and the equations of motion to generate an expression for the x-component of velocity u as a function of r. Ignore the effects of gravity. Fluid: p, H iP R; R, ƏP_ P2- P1 ax x2-X1arrow_forwardAn idealized incompressible fl ow has the proposed threedimensionalvelocity distributionV = 4xy2i + f (y)j - zy2k Find the appropriate form of the function f ( y ) that satisfi esthe continuity relation.arrow_forwardQ5 If, in an incompressible plane flow, the velocity component u = const, what can we say about the y-component of velocity? About the density?arrow_forward
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Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License