Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.8P
Consider a uniform flow with velocity
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A potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy . Determine the velocity in x-direction u=? and Stream Function SF=? ( x2 : square of x ; x3: third power of x ; y2: square of y , y3: third power of y)ANSWER: u= 3 x2 - 3 y2 SF= 3 x2 y - y3
Does the velocity potential exist for two dimensional incompressible flow prescribed by
u = x-4y; v = -(y+4x)?
If so determine its form (@) as well as that of stream function (u).
. Find the stream function associated with the two-dimensional incompressible,
possible flow with velocity components given by
a2
cos 0 and u, = -b 1+
--(1+)sino
a2
b1
r2
r2
Where a, and b are known constants.
Chapter 3 Solutions
Fundamentals of Aerodynamics
Ch. 3 - For an irrotational flow. show that Bernoullis...Ch. 3 - Consider a venturi with a throat-to-inlet area...Ch. 3 - Consider a venturi with a small hole drilled in...Ch. 3 - Consider a low-speed open-circuit subsonic wind...Ch. 3 - Assume that a Pitot tube is inserted into the...Ch. 3 - A Pilot tube on an airplane flying at standard sea...Ch. 3 - At a given point on the surface of the wing of the...Ch. 3 - Consider a uniform flow with velocity V. Show that...Ch. 3 - Show that a source flow is a physically possible...Ch. 3 - Prove that the velocity potential and the stream...
Ch. 3 - Prove that the velocity potential and the stream...Ch. 3 - Consider the flow over a semi-infinite body as...Ch. 3 - Derive Equation (3.81). Hint: Make use of the...Ch. 3 - Derive the velocity potential for a doublet; that...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the lifting flow over a circular cylinder...Ch. 3 - The lift on a spinning circular cylinder in a...Ch. 3 - A typical World War I biplane fighter (such as the...Ch. 3 - The Kutta-Joukowski theorem, Equation (3.140), was...Ch. 3 - Consider the streamlines over a circular cylinder...Ch. 3 - Consider the flow field over a circular cylinder...Ch. 3 - Prove that the flow field specified in Example 2.1...
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- Consider a flow field represented by the stream function ψ = (4+2) x3y - (6+2) x2y2 + (4+2) xy3. Is this a possible two-dimensional incompressible flow? Is the flow irrotational? Discuss the reasons against your findings.arrow_forward. The stream function for a two-dimensional incompressible flow is ax2 ay2 -+ bxy 2 2 Where a, and b are known constants. Find the velocity potential for the flow.arrow_forwardconsider the 2 dimensional velocity field V= -Ayi +Axj where in this flow field does the speed equal to A? Where does the speed equal to 2A?arrow_forward
- The stream function of a flow field is y = Ax3 – Bxy², where A = 1 m1s1 and B = 3 m-1s1. (a) Derive the velocity vector (b) Prove that the flow is irrotational (c) Derive the velocity potentialarrow_forwardIf the vorticity in a region of the flow is zero, the flow is (a) Motionless (b) Incompressible (c) Compressible (d ) Irrotational (e) Rotationalarrow_forwardQ1:- (a) Show that stream function exists as a consequence ofequation of continuity.(b) Show that potential function exists as a consequence ofirrotational flowarrow_forward
- Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction (into the page in Fig. There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. Calculate the velocity and pressure fields, and estimate the shear force per unit area acting on the bottom plate.arrow_forwardConsider a flow field represented by the stream functionψ=(4+1) x3y - (6+1) x2y2 + (4+1)xy3. Is this a possible two-dimensionalincompressible flow? Is the flow irrotational?Discuss the reasons against your findings.arrow_forwardConsider a flow field represented by the stream function ψ=24 x3y - 26 x2y2 + 24 xy3. Is this a possible two-dimensional incompressible flow? Is the flow irrotational?Discuss the reasons against your findings.arrow_forward
- Consider the steady, two-dimensional velocity field given by V = (1.3 + 2.8x)i+ (1.5 – 2.8y)j. 6. Verify that this flow field is incompressible.arrow_forwardConsider the following steady, incompressible, two-dimensional flow field: V=(1.1+ 2.8x +0.65y)i - (0.98 - 2.1x -2.8y)j. Calculate the accelaration field vector for the fluid particles in this systemarrow_forwardThe stream function o in a two-dimensional flow field is given as 9 = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. Find the potential flow function P(x, y) for this flow field with boundary condition 0 = 0 at x = 2, y = 1. (b)arrow_forward
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