Please show all work for a, b, & c!!! a) Which of the following velocity fields satisfy conservation of mass for an incompressible flow?Justify your answer and determine the stream function when possible.1. u = r³ siny, v = 3x² cos y2. u = r³ siny, v =-3x² cos y3. v 2r sin cos 0, v₁ = -r sin² 0=b) In two dimensions, a flow of density p exits from a source at the origin and moves radiallyoutward. Using conservation of mass, and assuming steady flow, show that the velocity musthave the form = r. Relate the constant C to the mass flow rate from the origin, ṁ.c) Repeat the previous part for a three-dimensional source, this time showing that the form ofthe velocity is v=

Answered: a) Which of the following velocity…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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1. If u- 3x'yr and v = -6x'y'r answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1). %3D
4. Consider a velocity field V = K(yi + ak) where K is a constant. The vorticity, z , is (A) -K (B) K (C) -K/2 (D) K/2
THREE DIMENSIONAL ( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).
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Problem 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.
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This question is from the subject "Fluid Mechanics"
Assumptions The flow is steady. The flow is incompressible. The flow is two-dimensional in the x-y plane V = (u, v) = (U, + bx) ỉ - byj %3D We are to calculate the material acceleration for a given velocity field. (None = b( U, +bx) a. y b? y = b( U, +by) ax b2 x (Uo +bx) = b y a, II
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