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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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.
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.
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.
Q4: The velocity components for a two dimensional incompressible flow are u = - 6xy, v=-3x2 + 3y2 1) Is the flow satisfied the continuity equation?. 2) Obtain an expression of stream function 3) Obtain an expression for the velocity potential if it is exsits.
An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.
2. Consider the two-dimensional time-dependent velocity field u(x, t) = (sint, cost, 0), in the basis of Cartesian coordinates. a) Determine the streamlines passing through the point x = 0 at the times t = 0, π/2, π and 3π/2. b) Determine the paths of fluid particles passing through the point x = 0 at the same times, to = 0, π/2, 7 and 37/2. Hence, describe their motion. ㅠ c) Find the streakline produced by tracer particles continuously released at the point xo = 0 and find its position at t = 0, π/2, π and 37/2. Hence describe its motion.

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