2.Show that the two-dimensional flow described (in meter-second units) by theequation y = x + 2x² – 2y² is irrotational. What is the velocity potential of the flow? If the densityof the fluid is 1.12 kg m and the piezometric pressure at the point (1, -2) is 4.8 kPa, what is thepiezometric pressure at the point (9, 6)?-3

Answered: Image /qna-images/answer/97153acf-32b5-4d24-b6e2-f8e474bed70b.jpg

Answered: Show that the two-dimensional flow…

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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please explain how the derivative first part clearly
on 2 A two dimensional flow field is defined by y = y-x². Sketch the streamlines: y = 0, y = 2 and y = 3 %3D %3D
please answer quickly
The stream function o in a two-dimensional flow field is given as 9 = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. Find the potential flow function P(x, y) for this flow field with boundary condition 0 = 0 at x = 2, y = 1. (b)
Consider irrotational flow past a stationary sphere of radius R located at the origin. In the limit r→∞, the velocity field v = U2, as in Fig. 8-6 in the book. (a) Calculate the velocity field v assuming potential flow given by v = Vo(r, 0, 0), where the potential can be assumed to be independent of the azimuthal coordinate and vo= 0. Here, since ə rde Ə Ər for large r/R, look for solutions of the form = f(r) cos 0. Assume a no-penetration boundary condition at the surface of the sphere. (b) Calculate the pressure P and the drag force due to pressure. Vr = U cos 0 and Vo = -U sin 0
Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.
Let the flow of a fluid of density ρ = 1000 kg m^-3 defined by the velocity field v = xy i + yz j + zx k ms-1. Is this runoff irrotational? What is the accumulation rate per volume unit at point (1,1,1)?

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