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

Section: Chapter Questions

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The two components of the velocity vector are given as Vx = –ay/(x2+ y2)1/2 and Vy = ax/(x2+ y2)1/2 where a is a constant in cm/s. Find the vorticity of a fluid element located at x = y = 1 cm. [Ans.: 1.41a k ].
If the vorticity in a region of the flow is zero, the flow is (a) Motionless (b) Incompressible (c) Compressible (d ) Irrotational (e) Rotational
The velocity components of an incompressible, two-dimensional field are given bythe following equations: u(x,y) =y^2 -x (1+x) v(x,y) = y(2x+1) Show that the flow field is (a) irrotational and (b) satisfies conservation of mass.
It is given as u = 2 (1 + t), v = 3 (1 + t), w = 4 (1 + t) in a flow field. Accordingly, find the velocity and acceleration values at the points (3,2,4) at t=2 seconds.
If the velocity field, V=3y2 i. Which of the following is NOT TRUE? Select one: The flow is steady The flow is irrotational The flow is horizontal d. The flow is incompressible Consider the velocity field, V=(x2+y2-4)i+(xy-y)j. Which of the following is not a stagnation point? A stagnation point is a point in the velocity field where the velocity is 0. (2, 0) (-2, 0) (1, √3) (-1, √3)
1. Find the equation of a streamline that passes through the point P(1, 4, -2) in the field E=2e5x[y(5x+1)ax+xay]E=2e5x[y(5x+1)ax+xay].
The velocity field is given as u=y-1 and v=y-2. The units of u and v are m/s and the units of x and y are meters. a) Draw the stream line passing through the point (x,y)=(4.3). b) Determine the streakline passing through the point (x, y) = (4,3) and compare it with the streamline. c) Determine whether the current is revolving or not.
A 2D incompressible velocity field is defined by . If both u and v are 0 at point (x = 0, y = 0), determine a) v component of the velocity and b) an expression for pressure field. Assume gravity is in the – y-direction and pressure is 0 at point (x=0, y=0). The flow is defined by: u=2(x2-y2)
A velocity profile for water is given as a function of x, y and z. How can we determine if the profile is a physically possible flow field? A) If the sum of the derivatives of each component with respect to their flow direction = 0. B) If the flow is irrotational. C) If the vorticity equals 0. D) If we can determine a velocity potential.
two-dimensional velocity field u =xt + 2y and v =xt^2- yt x=1 meter y= 1 meter and t= 1 second Find the acceleration where it is.?
Velocity components in the flow of an ideal fluid in a horizontal plane; Given as u = 16 y - 12 x , v = 12 y - 9 x a) Is the current continuous?(YES OR NO) b) Can the potential function be defined?(YES OR NO) c) Find the unit width flow passing between the origin and the point A(2,4). (y(0,0)=0) d) Calculate the pressure difference between the origin and the point B(3;3).
24. In a two-dimensional incompressible flow, the component Vx of the velocity vector is given as Vx = –x2y. Find Vy. [Ans.: Vy = xy2 + C].

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