At a depth of 1000 m in an ocean (a) What is the absolute pressure ? (b) What is the gauge pressure ? © Find the force acting on the window of area `20cmxx20cm` of a submarine at this depth the interior of which is maintained at sea level atmospheric pressure. (the density of sea water `=1.03xx10^(3)xx10^(3)kgm^(-3),g=10ms^(-2))`

Explanation

Depth in sea water h = 1000 m
Density of sea water `rho=1.03xx10^(3)xx10^(3)kgm^(-3)`
Acceleration of gravity `g=10ms^(-2)`
Atmospheric pressure at sea water surface,
`P_(a)=1.01xx10^(5)Nm^(-2)`
(a) Absolute pressure at h depth,
`P=P_(a)+hrhog`
`=1.01xx10^(5)+1000xx1.03xx10^(3)xx10`
`1.01xx10^(5)+103xx10^(5)`
`=104.01xx10^(5)Pa`
`=104atm[because10^(5)Pa=1atm]`
(b) Gauge pressure `P-P_(a)=hrhog=P_(g)`
`therefore P-P_(a)=1000xx1.03xx10^(3)xx10`
`P_(g)=103xx10^(5)Pa`
where gauge pressure `P_(g)=P-P_(a)`
`=103 atm`
The pressure outside the submarine is
`P=P_(a)+hrhog` and the pressure inside it is `P_(a)`
Therefore The net pressure acting on the window is gauge pressure `P_(g)=rhogh`
The area of the windown
`A=20cmxx20cm`
`=400cm^(2)`
`=400xx10^(-4)m^(2)`
`therefore` The force acting on Windown,
`F=P_(g)A`
`=103xx10^(5)xx400xx10^(-4)`
`=41200xx10`
`thereforeF=4.12xx10^(5)N`