Given the velocity potential f of a flow, find the velocity V = Vf of the...
number 4 parts a b and c The symbols Vf, V.. bols vf, V az oy F, and V x F are defined by Of = grad f 7. F = div F VXF = curl F After eq. (3.12) is memorized, formulas (3.13) through (3.15) venient ways of remembering the expressions for gradient, diverge just operate with V as though it were a vector. Henceforth, we breviations frequently. EXERCISES 1. If f(x,y,z) = x²y + z, what is f(2,3,4)?...
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
2) A flow field has velocity field given by: u= x2 - y2, v= -2xy 1. Prove that the flow is irrotational 2. Determine the stream function, 3. Find the potential function, 4. Create a plot of the flow net diagram
The Velocity field of a flow is given by V=4xy^2i + 4x^2yj. a) calculate the stream function and the velocity potential b) find the equation for the stream line passing through point x=1, y=1. plot this function accurately c) find the equation for the equipotential line passing through point x=1, y=1. plot this function accurately on the same graph as part b.
Chapter 7, Section 7.2. Question 20 Find the PDF of the given CDF F(x) =0 x58 F(X) = 1 - 27 28 for and Click here to enter or edit your Click here to enter or edit your answe for X8 Policy | 2000-2020 John Wiley & Sons, Inc. All Rights Reserved. A Division of John Wiley Sons, Inc.
Given the velocity field V =107 +(x + y2)7-2xyk [m/s] Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of (x, y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m?
Гa b c] Let A = d e f . Assume that det(A) = -11, find Igni Ta gol (a) det(2A) (b) det(A-1) c) det(3A-1) (a) det((3A) – 1) (e) detone (a) det(2A) = Click here to enter or edit your answer - 22 (b) det (A-1) = Click here to enter or edit your answer (c) det(3A-1) = Click here to enter or edit your answer (d) det((3A)-1) = Click here to enter or edit your answer a gol...
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given by u =-Cy and v = Cx , where is a constant. (i) Does this velocity distribution satisfy continuity? If yes, what is the stream function y? (8 marks) (ii) Analyse whether the flow is rotational or irrotational. What is the velocity potential o ? (4 marks) (iii) Sketch several y and © lines (if exist) of the flow field. Briefly explain how you...
Chapter 6, Section 6.5, Question 06 Consider the given system of equations. (a) Find a fundamental matrix Express X (t) as a 2x2 matrix of the form x(t) = where vi-Ci ) s the eigen vector associated with the complex eigen value λί V11 Re (eht vi lm (e,%) Click here to enter or edit your answer (b) Find the fundamental matrix eAr (b) Find the fundamental matrix eAr Click here to enter or edit your answer Click if you...
2. The velocity potential for a spiral vortex flow is given by φ-2nInr-2-9, where A (positive) is the sink strength and Γ is the vortex strength (1) Find the expression of stream function. (2) The plot of stream function is shown in the following figure. Prove the angle,a, between the 2Tt velocity vector and the radial direction is constant throughout the flow field. (FYI, this spiral is called Logarithmic spiral.) .y