3.3. The velocities at a point in a fluid in the Eulerian system are given byux+y+z+s=2(x + y + z) +- 1W = 3(x + y + z) + iShow that the displacements of a fluid particle in the Lagrangian system arex=2x-30 120 + f (x + y + zo + 1')e" - r²+++--y= -xo+yo-zo + (xo + yo + zo + 1)e³ - f - 38z = −x − y + zo + (x + yo +20 + 1)e" - 11 - 11² - 2-

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Answered: 3.3. The velocities at a point in a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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3.1. The velocity at a point in a fluid for a one-dimensional flow may be given in the Eulerian coordinates by u == AxBt. Show that x = f(x, t) in the Lagrange coordinates can be obtained from the Eulerian system. The in- itial position of the fluid particle is designated by x) and the initial time to = 0 may be assumed.
navier stokes
fluid mechanics
Given the Eulerian velocity vector field: V = 3ti + xzj + ty²k Find the total acceleration of a particle av av av W дх' ду' ду Hint: u V
Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow
1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP|B² Vz = 2µL B a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B? v, = 2μL Problems 11 - 2B --– €. (a) 2B (b) Figure 1.3. Flow between parallel plates. b) Calculate the volumetric flow rate by using the velocity distributions given above. What is your conclusion? 2|A P|B³W Answer: b) For both cases Q = 3µL
I need help with C and D. I want to see detailed steps.
Tp = Fq +°P/Q• (1) Here ip/Q is the "position of point P relative to point Q." Similarly the velocities of the two points are related by õp = bq + Up/Q- (2) The quantity õp/Q is the velocity of point P relative to point Q. I want you to use these ideas to solve the following problems. 1. The figure below shows a view from above of a large boat in the middle of the ocean. So that the crew on the ship can get exercise on long journeys, there is a circular walking/running track on the back deck. CA B- -D Suppose that the radius of the track is R = 6 m, and a person is running on the track at a constant speed of v = 3m/s as measured with a stopwatch by a crew-mate on board the ship. Suppose the runner is running counter-clockwise around the track when viewed from above. Write the velocity vector of the runner in terms of basis (ê1, ê2) as perceived by a crew-mate on the ship. (a) What is the velocity vector when the runner is at point A? (b) What is the velocity vector when the runner is…
2. The velocity components expressed in m/s in a fluid flow is known to be: 2 u= 2yzt v=xy W=4xzt² Find the acceleration of a fluid particle at point, P (2m,1m,1m) when time is 2 s.
4
1. A flow in the x-y plane is given by the following velocity field: u =3 and v=6m/s for 0
ND (h2s-h1) (h2s-h1)-(h2s - h2) Derive Equation (2.46) 1 - (h2s - h2)/(h2s - h1) 1 1 + (P01 − P02)/(P2 — P1) * (2.46)

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