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# Pressure at Depth Calculator

## Hydrostatic Pressure / Pressure at Depth Formula:

The deeper the object is situate in a fluid the higher the pressure is exerted on the object in at sea a depth is calculated:

Ptotal = Patmosphere + Pfluid    .(1).

Where:

Patmosphere: The atmosphere pressure.

Pfluid: Pressure on an object submerged in a fluid.

Ptotal: The total pressure.

A Pressure on an object submerged in a fluid is calculated with the below equation:

Pfluid= r * g * h   .(2).

where:

Pfluid= Pressure on an object at depth.

r=rho= Density of the sea water.

g= The acceleration on of gravity = the gravity of earth.

h= The height of the fluid above the object or just the depth of the sea.

To sum up the total pressure exerted to the object we should add the atmospherics pressure to the second equation as below:

Ptotal = Patmosphere + ( r * g * h ). (3).

In this calculator we used the density of seawater equal to 1030 kg/m3 3 as per the  “Beicher, Robert J. Physics for Scientists and Engineers. Orlando: Saunders College, 2000.”

## How does sea water pressure change with depth?

 Depth (m) Pressure (Bar) Depth (m) Pressure (Bar) 1 1,11094 30 4,0298 10 2,0187 40 5,0353 20 3,0243 50 6,0408

## How to calculate gauge pressure at sea depth?

The fluid pressure is also called “gauge pressure” is the force applied on surface by a fluid (liquid or gas) without considering the atmospheric pressure.
The pressure gauge is equal density multiplied by depth and acceleration.

Since the gauge pressure is equal to the absolute pressure minus the atmospheric pressure.
Pgauge= Pabsolute-P atmospheric= r * g * h

In vacuum condition (patm=0 bar v) the absolute pressure will be equal to the gauge pressure.

The density of the sea water changes most importantly by salinity, pressure and temperature:

• As the temperature increase so the density of the water will decrease as the fluid will expand with temperature.
• Sea water is compressible but not like the gas. As the pressure increase consequently the density of the sea water will increase.
• In addition to pressure and temperature effect, the salinity increase the density of water will increase.

## Pressure at Depth Calculation Examples:

Example 1:

A person is diving in a lake in the depth of h= 8 m and the water density of the lake is 998 kg/m3. therefore Calculate the absolute pressure and the gauge pressure.

Solution:
Pfluide= Pgauge = rgh.
= 998 kg/m39.8m/s8m.
=78243 Newtons/m2.
= 78 kPa.

Therefore the total pressure would be:
Ptotal= Pgauge + Patm.
=78243.2+ 101 325 .
=179568.2 Pa (Pascal).
=179.5682 kPa.

Exemple 2 :

Calculate the pressure at the bottom of swimming 10 meter in depth. The density of the water of the pool is 1000 kg/m3. Calculate the absolute pressure and the fluid pressure.
Solution:

Pfluide= Pgauge = rgh.
= 1000 kg/m39.8m/s10m.
=98000 Newtons/m2.
= 98 kPa.

as a result the total pressure is equal to :
Ptotal= Pgauge + Patm.
=98000+ 101 325 .
=199325 Pa (Pascal).
=199.325 kPa.