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).
3. The velocity components of a two-dimensional incompressible fluid flow are prescribed as v=-3x²² u=-1 i) Determine the stream function. ii) Using excel plot the stream function for y=-5 and y=-20 from x = 0 to x = 5.
Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 s
a. Derive an equation for the material acceleration vector.b. Obtain the vorticity vector for the velocity field.c. Is the flow rotational or irrotational? Show through your derivation.d. Is the flow incompressible or compressible? Show through your derivation.
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.
The velocity components of a flow field are given by: = 2x² – xy + z², v = x² – 4xy + y², w = 2xy – yz + y² (i) Prove that it is a case of possible steady incompressible fluid flow (ii) Calculate the velocity and acceleration at the point (2,1,3)
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
1. For a velocity field described by V = 2x2i − zyk, is the flow two- or threedimensional? Incompressible? 2. For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0, find the slope of the streamline passing through the point [2, 4] at t = 2. 3. Find the angle the streamline makes with the x-axis at the point [-1, 0.5] for the velocity field described by V = −xyi + 2y2j
Question 1 Consider a steady, two dimensional, incompressible flow of a Newtonian fluid with velocity field: u = -2xy v = y² – x² a) Show that this flow model satisfies the continuity relation. b) Obtain expressions for the fluid accelerations in the x and y directions. c) Find the pressure distribution P(x, y), if the pressure at the point x = y = 0 is Po. Neglect gravity.

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