# Finding the total pressure acting on a submarine

Hello I'm having trouble with answering this question: Certain submarines are capable of speeds in excess of 30 knots. What is the total pressure sensed at the nose of a submarine if the vessel is at periscope depth (5 m) and a speed of 30 knots? (Assume a constant sea-water density of 1030 kg/m3.) What height would the captain read on a mercury manometer that sensed this total pressure?
I know the equations Po=Ps + (1/2)(rho)(V)^2 and dP=(rho)(g)(dh) but am having trouble finding the static pressure in order to find the total pressure.

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A depth of 0m corresponds to air pressure (~1.013*10^5 N), your equation for dP allows to add the 5m of water between nose and surface.

The second equation should be enough. The submarine will experience this pressure over its surface area. So the mercury manometer will sense this pressure. The hard part would be to calculate the "lift" of the submarine, for which you could use Newton's method.

Keep in mind that the nose may see a stagnation point, you won't necessarily see the same total pressure (static and dynamic) as other parts of the vessel.