Calculate the differential pressure in kPa across the hatch of a submarine 320m below the surface of the sea. Assume the atmospheric pressure at the surface is the same as in the submarine. (S.G. of sea water =1.025).

Gauge pressure is the pressure above the atmospheric pressure. If we consider gauge pressure for finding pressure differential then no need to consider atmospheric pressure as they will cancel out. According to hydrostatic law, pressure varies in the z direction only.

Given:

Height of the hatch is 320 m

Surface gravity of the sea water is 1.025.

Density of water 1000 kg/m³.

Calculation:

Step1

Density of sea water is calculated as follows:

[tex]S.G=\frac{\rho_{sw}}{\rho_{w}}[/tex]

Here, density of sea water is[tex]\rho_{sw}[/tex], surface gravity is S.G and density of water is [tex]\rho_{w}[/tex].

Substitute all the values in the above equation as follows:

[tex]S.G=\frac{\rho_{sw}}{\rho_{w}}[/tex]

[tex]1.025=\frac{\rho_{sw}}{1000}[/tex]

[tex]\rho_{sw}=1025[/tex] kg/m³.

Step2

Difference in pressure is calculated as follows:

[tex]\bigtriangleup p=rho_{sw}gh[/tex]

[tex]\bigtriangleup p=1025\times9.81\times320[/tex]

[tex]\bigtriangleup p=3217680[/tex] pa.

Or

[tex]\bigtriangleup p=(3217680pa)(\frac{1kpa}{100pa})[/tex]

[tex]\bigtriangleup p=3217.68[/tex] kpa.

Thus, the pressure difference across hatch of the submarine is 3217.68 kpa.