please do all parts otherwise skip I'll UPVOTE A steady, incompressible, two-dimensional velocity field is given by V = (u, v) =Axi – Ayj; the units of velocity are m/s; x and y are given in meters; A = 0.3 s¯!.a) Obtain an equation for the streamlines in the xy plane.b) Determine the velocity of a particle at the point (2, 8).c) If the particle passing through the point (xo, Yo) is marked at time t =determine the location of the particle at time t = 6 s.d) What is the velocity of this particle at time t = 6 s?= 0,e) Show that the equation of the particle path (the path line) is the same as theequation of the streamline.

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Answered: A steady, incompressible,…

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) In a flow of fluid, velocity field is given by u=-y, v=x, w=0. a) Find the orbitals. b) Obtain streamlines at time t. c) Determine the output line belong to point A(1,0,0) and time t=p/2
This problem will show you how to obtain the pathline and the streamline for a velocity field. A velocity field is given by u=(ax_1 t)i −(bx_2)j , where a=0.1^s−2 and b=1s^−1. (a) For the particle that passes through the point (x1,x2) = (1,1) at instant t = 0, get the equation of the pathline during the interval from t = 0 to t = 3s. Plot it roughly by hand(b) Get the equations of the streamlines through the same point at the instants t = 0,1, and 2s. Plot it roughly by hand
1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.
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)
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.
The velocity field of a flow is described by V-›= (4x) i-›+ (5y + 3) j-›+ (3t2)k-›. What is the pathline of a particle at a location (1 m, 2 m, 4 m) at time t = 1 s?
(a) State the equation describing the condition at streamline boundary for a two-dimensional flow with velocity V and displacement ds Using the equation, derive the equation of a streamline given by Eq. (4.1): ) (See attached images) (b) A steady, incompressible, two-dimensional velocity field is given by Eq. (4.2) : (see attached images) Where: the x- and y-coordinates are in metres and the magnitude of the velocity is in m/s. Calculate the material acceleration at the points of (x = 2, y= 3)
The actual path traveled by an individual fluid particle over some period is called a (a) Pathline (b) Streamtube (c) Streamline (d ) Streakline (e) Timeline
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.?
A flow is described by the flow field of vec(V)=A(1+Bt)hat(i)+Ctyhat(j), where A=1 m/s, B=1 s -1 , and C=1 s -2 . The unit for the coordinates is meters. a. Plot the pathline that passes through the point (x=1 m, y=1 m) at time t=0 . b. Compare the streamlines through the point (x=1 m, y=1 m) at time t=0, 1, and 2 s. c. Calculate the acceleration at time t=0 along the streamline passing the point (x=1 m, y=1 m) at time t=0 .
Under what condition are all the three curves; pathline, streakline and streamline, the same
Consider a velocity field where the x and y components of velocity are given by u = cx and v = -cy, where c is a constant. Obtain the equations of the streamlines.

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