How Does Water Pressure Affect a Submarine at Various Depths?

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SUMMARY

The discussion centers on the effects of water pressure on a homemade submarine at a depth of 9.7 meters. The pressure at this depth can be calculated using the equation P2 = P1 + pgh, where P1 is atmospheric pressure (approximately 101,325 Pa), p is the density of seawater (approximately 1025 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and h is the depth (9.7 m). The net force required to dislodge the duct tape can be determined by calculating the pressure difference across the tape and the area of the hole. Additionally, the velocity of water exiting the small end of a funnel can be calculated using the principle of conservation of energy and the continuity equation.

PREREQUISITES
  • Understanding of fluid mechanics principles
  • Familiarity with pressure calculations in fluids
  • Knowledge of the continuity equation in fluid dynamics
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the pressure at a depth of 9.7 meters using the formula P2 = P1 + pgh
  • Determine the net force acting on the duct tape using the area of the hole and the pressure difference
  • Explore the continuity equation to find the velocity of water exiting the funnel
  • Investigate the implications of pressure changes on submarine design and safety
USEFUL FOR

This discussion is beneficial for students studying fluid mechanics, engineers designing submarines, and anyone interested in the practical applications of pressure in underwater environments.

biomajor009
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Homework Statement


Your homemade submarine has a circular hole with a diameter of 14 cm in its side. You decide to plug the hole by taping over it with watertight duct tape. This works pretty well while you are exploring the ocean at shallow depths, but you find that as soon as you reach a depth of 9.7 meters the duct tape is dislodged.
(a) What is the pressure of the ocean water at this depth?
(b) What net force was needed to dislodge the duct tape? You may assume that the interior of the sub was at atmospheric pressure.
(c) When the duct tape is dislodged, ocean water begins to shoot into the sub at a speed of 7.1 m/s. You grab something to put over the hole, but all you have handy is a funnel. The large end of the funnel is big enough to cover the hole, while the small end has an opening with a diameter of 2.2 mm. If you place the funnel over the hole, how fast will water shoot out of the small end of the funnel? Would you want to plug up the small end by putting your hand over it?


Homework Equations





The Attempt at a Solution


I'm having trouble getting past the first part of the question. I tried using the equation
P2 = P1 + pgh, but I don't know what P1 should be. Am I even using the right equation?
 
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P1 is the pressure at the surface
 

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