P = ρgh

Steps to Solve

1. Identify the variables
   In the equation $P = \rho g h$, we have:

• $P$: Pressure
• $\rho$: Density of the fluid
• $g$: Acceleration due to gravity (approximately $9.81 , \text{m/s}^2$)
• $h$: Height of the fluid column

2. Explain the relationship
   The equation shows that pressure increases with an increase in any of the variables $\rho$, $g$, or $h$. This means:

• If the fluid density $\rho$ increases, for the same height, pressure $P$ increases.
• If the acceleration due to gravity $g$ increases (in a different planet, for example), pressure $P$ will also increase for the same height and density.
• As the height $h$ of the fluid increases, pressure $P$ also increases if density and gravity remain constant.

3. Pressure at a specific depth
   To find the pressure at a specific height, rearrange the formula to solve for $P$.
   For example, if $\rho = 1000 , \text{kg/m}^3$ (water), $g = 9.81 , \text{m/s}^2$, and $h = 10 , \text{m}$:
   $$ P = \rho g h = 1000 \times 9.81 \times 10 $$

4. Calculating pressure
   Now calculate:
   $$ P = 1000 \times 9.81 \times 10 = 98100 , \text{Pa} $$

This value represents the pressure at a height of 10 meters of water.