FLUIDS: Gauge Pressure as a Function of Fluid Depth

Q: What is the gauge pressure (in psi) at the bottom of a body of water that is 18.7 ft deep?

A: Pressure in Pascals ( P ) = ( ρ )( g )( h ), where ρ is the density of the fluid medium in units of mass per unit volume ( m / V ), the gravitational constant of acceleration ( g ) = 9.8 m/s², and h is the distance in meters ( m ) a gauge is positioned below the fluid’s surface.

Pressure is defined as force per unit area ( F / A ). The SI Unit of force is the Newton ( N ) in units of kg*m/s², and area ( A ) is square meters ( m² ). If we multiply ( ρ )( h ), we are left with units of ( m / A ). Recall that pressure ( P ) = force per unit area, and force = ( m )( g ); therefore, ( m / A )( g ) = ( F / A ). 

P = ( ρ )( g )( h ) will give us the gauge reading. Let’s first convert 18.7 ft to meters ( m ):

( 18.7 ft )( 0.3048 m / 1 ft ) = 5.70 m.P = ( ρ )( g )( h ) = ( 997 kg / m³ )( 9.8 m/s² )( 5.70 m ) = 55.7 kP.