(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The velocity vector for a flow is u = (xt, yt, -2zt). Given that the density is constant and that the body force is F = (0,0,-g) find the pressure, P(x,t) in the fluid which satisfies [tex]P = P_0(t) [/tex] at x = 0

2. Relevant equations

Euler's equation: [tex] \frac{Du}{Dt}=-\frac{1}{\rho}\nabla P + F [/tex]

3. The attempt at a solution

[tex] \nabla P = \rho(-x-xt^2, -y - yt^2, 2z - 4zt^2 - g) [/tex]

How do you get P from this. Back of the book gives

[tex] P = - \frac {1}{2} \rho (x^2+y^2)(1+t^2) + \rho z^2(1-2t^2)-\rho gz + P_0(t) [/tex]

How did they get that?

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# Homework Help: A solution of Euler's equation

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