Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 2, Problem 2.9P
Is the flow field given in Problem 2.5 irrotational? Prove your answer.
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Consider 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.
If a flow field is compressible, what can we say about the material derivative of density? What about if the flow field is incompressible?
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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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
- For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0: (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the x-component of the acceleration vector.arrow_forwardAn Eulerian velocity vector field is described by V = 3xzj + yk, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is the flow one-, two- or three-dimensional? (b) Is the flow compressible or incompressible? (c) What is the acceleration following a fluid particle? (d) If gravity and viscous forces can be neglected, what is the pressure gradient?arrow_forwardConsider steady, incompressible, parallel, laminar flow of a viscous fluid falling between two infinite vertical walls. The distance between the walls is h, and gravity acts in the negative z-direction (downward in the figure). There is no applied (forced) pressure driving the flow—the fluid falls by gravity alone. The pressure is constant everywhere in the flow field. Calculate the velocity field and sketch the velocity profile using appropriate nondimensionalized variables.arrow_forward
- For an unsteady, compressible flow field that is two-dimensional in the xy-plane and in which temperature and density variations are significant, how many unknowns are there? List the equations required to solve for these unknowns. (Note: Assume other flow properties like viscosity, thermal conductivity, etc., can be treated as constants.)arrow_forwardProblem N-S 2 A velocity field is described by the following equations: 10y -10x and w=0 u = x²+y2 ' V = x²+y2' (a) Is this flow compressible or incompressible? (b) Find the pressure gradient. Assume frictionless flow in the z-axis, the density is 1.2 kg/m³, and the z-axis is aligned with gravity. Also assume the normal and shear effects are negligible.arrow_forward1 (a) If a flow field is compressible, what can you say about the material са derivative of density? What about if the flow field is incompressible? Explain your answer.arrow_forward
- 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_forwardConsider a vortex filament of strength in the shape of a closed circularloop of radius R. Obtain an expression for the velocity induced at thecenter of the loop in terms of and R.arrow_forwardProblem 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_forward
- Consider the pipe annulus sketched in fig. Assume that the pressure is constant everywhere (there is no forced pressure gradient driving the flow). However, let the inner cylinder be moving at steady velocity V to the right. The outer cylinder is stationary. (This is a kind of axisymmetric Couette flow.) Generate an expression for the x-component of velocity u as a function of r and the other parameters in the problem.arrow_forwardAn Eulerian velocity vector field is described by V = 2x2yi − 2xy2j − 4xyk, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is the flow one-, two- or three-dimensional? (b) Is the flow compressible or incompressible? (c) What is the x-component of the acceleration following a fluid particle? (d) Bonus question: Is the flow irrotational?arrow_forwardA viscous incompressible Newtonian fluid is contained between two fixed parallel plates inclined at an angle 0, and the flow is driven by both constant pressure gradient E = constant) and gravity. The distance between the two plates is 2H and the chosen system of coordinates is shown in the figure. Assuming steady, 2D, and parallel flow (v = w = 0) and using differential analysis: (a) Show that the flow is fully developed using continuity equation; and (b) Find the velocity profile u(y) in terms of ,H,P,g,0,H de using Navier-Stokes equations with appropriate boundary conditions. 211arrow_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