# Particle displacement from pressure [closed]

Is this correct? I'm looking for other sources of the result.

If pressure at a point is sinusoidal

$$p=p_0 sin(\omega t)$$

then particle displacement is

$$\boldsymbol{s} = {1 \over {\omega^2 \rho}} \boldsymbol\nabla p$$

where $$\rho$$ is the fluid's density.

I derived it by taking the 2nd time integral of particle acceleration $${\boldsymbol{a}} = {-1\over\rho} \boldsymbol\nabla p$$.

• It looks good, as long as you are not accounting for any viscous effects, which would change the conservation of momentum equation you are using. Jan 24 at 13:52