# Density gradient in a fluid

1. Jun 1, 2009

### ponjavic

Should be a simple question really can not understand why I am not able to get my head around it though. Assume an isothermal stationary fluid under the influence of gravity. Navier stokes reduces to
$$\frac{dP}{dy}=-\rho g$$
Differentiating the equation of state $$P=\rho R T$$
$$\frac{dP}{dy}=\frac{d\rho}{dy}RT = -\rho g$$
Shouldn't the pressure gradient and the density gradient be linear under gravity? That's what I get from my simulations

Edit: Nevermind fixed my simulation, gradient is obviously exponential

Last edited: Jun 1, 2009