Question

Consider a planet entirely constituted by water,

How the pressure P(h) varies in function of the deepness h?

Answer 1

`p = g*\rho*h+p_(atm)`

Step-by-step explanation:

The pressure will vary with the hydrostatic pressure (
`g*\rho*h`), which is the pressure of a column of liquid with height h, the total pressure under the water will be the hydrostatic pressure plus the atmospheric pressure, the equation is:

`p = g*\rho*h+p_(atm)`

Where:

• 
  `p=` total pressure.
• 
  `g=` gravitational acceleration.
• 
  `\rho=` fluid density.
• 
  `h=` height.
• 
  `p_(atm)=` atmospheric pressure.

In this planet,
`g\textrm{ and } p_(atm) \textrm{ could be different than in the Earth.}`

This is a reasonable estimation because many liquids can be considered incompressible, then we can assume a constant density throughout the liquid.