b) The velocity potential for a flow is Ø = In (x2 + y2)1/2 i. Show that this function satisfies Laplace's equation, ii.

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B The Velocity Potential For A Flow Is O In X2 Y2 1 2 I Show That This Function Satisfies Laplace S Equation Ii 1 (38.74 KiB) Viewed 37 times

b) The velocity potential for a flow is Ø = In (x2 + y2)1/2 i. Show that this function satisfies Laplace's equation, ii. Is this flow rotational or irrotational flow? explain why, iii. Find the stream function ф (x, y), and iv. Determine the velocity components u and v at point P (1,3). Formula др at др др др и + И. +w дх ду дz •+P (ди до дw + дх ду дz. = 0 1 др ди ди ди ди + и - + + + at ду дz -- [а?а а?а а?u +9х+у + + рах |дх?" ду?" дz? | и = дф дф ду дх = 1 до дф де Il т до др у = - дх дф ду Ve = -. до 1 дф де где ф= Uо у ф ІІ г -Inr 2п u sine 2п т а ф= в + pv? + pght = p + 5ри? + Рgh р. pv