(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A solution of Euler's equation

**Physics Forums | Science Articles, Homework Help, Discussion**