A research submarine has a 40cm diameter window that is 8.4cm thick. The manufac

Question

A research submarine has a 40cm diameter window that is 8.4cm thick. The manufacturer says the window can withstand forces up to 1.1x10^6 N. What is the submarine's maximum safe depth in sea water? The pressure inside the submarine is maintained at 1.0 atm. I tried 3457.37m, 3.46x10^3 m. 3.78m, and 3.77x10^6m A research submarine has a 40cm diameter window that is 8.4cm thick. The manufacturer says the window can withstand forces up to 1.1x10^6 N. What is the submarine's maximum safe depth in sea water? The pressure inside the submarine is maintained at 1.0 atm. I tried 3457.37m, 3.46x10^3 m. 3.78m, and 3.77x10^6m I tried 3457.37m, 3.46x10^3 m. 3.78m, and 3.77x10^6m

Explanation / Answer

Radius of window = 20 cm or 0.2 m

Considering the window to be circular its area is A = r2 = D2/4 = 3.14 x 202 x 10-4 = 0.125664 m2

Assuming the density of seawater to be 1025 kg/m³, pressure increases by 1 atm with each 10 m of depth.

Pressure = hg = 10 x 1025 x 9.8 = 100450 = 1.00 x 105 Pa OR 1 atm for a depth of 10 meters.

Pressure = Force / area

The force experienced by the window is difference in pressure from outside and intside into area

F = ( Pout - Pin ) x A 1 atm = 101325 Pa (S.I unit of pressure)

F =  ( hg - 101325 ) x A

1.1 x 106 = ( h x 1025 x 9.8 - 101325 ) x 0.125664

h x 1025 x 9.8 - 101325 = (1.1 x 106 ) / 0.125664 = 8753501.401

h x 1025 x 9.8 = 8753501.401 + 101325 = 8854826.401

h = 8854826.401 / (1025 x 9.8) = 881.516 m

The maximum depth the submarine can reach is 881.516 meters.

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