Question

1. A submarine dives from the surface of the ocean to a depth of 3500 feet ( 1foot= 0.305 meters) .

a) what pressure increase does the submarine experience?

b) at this depth of 3500 feet, what is the force (in units of N) on the hatch which has an area of 0.6 m2 ? Take the density of sea water to be 1030 kg/m3 ( It is a good assumption to presume that sea water has essentially constant density, independent of depth)

2. Someone you know is in the hospital and requires the intravenous feeding of nutrients. The blood pressure in the vein of the person is 20 mmHg. This means that the pressure in the vein is 20mmHg greater than atmospheric pressure. What is the Minimum height above the insertion point for the needle into the vein that the nurse must hang the nutrient supply bottle to ensure that the nutrients flow into the patient ? Assume that the fluid nutrients have the density of water. ( Here Hg stands for the chemical symbol of mercury and is not height times gravitational acceleration.)

Answer 1

The pressure on the submarine is

$P= P ^{_ {0}} + h \rho g$

P₀ = Atmospheric pressure = $1.013\times 10^{5}N/m^{2}$

h =depth = 3500feet =1067.5m

g= 9.8m/s²

$\rho =1030kg/m^{3}$

$P= 1.013 \times 10^{5}+1067.5\times 1030\times 9.8$

$P =108.76645\times 10^{6}N/m^{2}$