In the book the hunt for red october a russian submarine is described which uses a silent "caterpillar" drive instead of a propeller. even though the propulsion system is very quiet, the submarine may still make a lot of noise if it goes too fast. the reason is that, if the speed of the submarine is too great, the static pressure at the point of maximum velocity over the submarine will drop below the vapor pressure for saturated water and the water will boil or cavitate. when the bubbles thus formed collapse, they make a lot of noise, making it easy to detect the submarine. the flow will not cavitate as long as the static pressure is greater than the vapor pressure of saturated water, p_v. for the purposes of this problem, assume the ocean has a uniform density rho = 1000 kg/m^3, atmospheric pressure acting on the surface of the ocean is p_a = 101 kpa (1.01 times 10^5 n/m^2), the acceleration due to gravity is g = 9.81 m/s^2, the vapor pressure of saturated water at 12 degree c is p_v = 1.4 kpa, and that the entire ocean has a uniform temperature of 12 degree c.

if the maximum velocity over the surface of the submarine is 2.0 times the freestream velocity, how fast can the submarine go at a depth of 100 m without cavitating? in order to go faster without being detected should the submarine increase or decrease its depth? explain your answer.