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Find torque exerted by the sea on a submerged submarine's three escape hatches

See attached diagram.

Three emergency escape hatches are on a submarine submerged in sea water whose density is D=1025 kg/m^3. Each hatch is rectangular, having width W= .85 m, length L= 1.2 m with its hinge of length W along one side.

See attachment for orientation for Parts a, b, and c.

PART a. The Deck Hatch is in a horizontal plane at depth H below the sea surface. Find the torque about an axis through the hinge, exerted on the hatch by the sea.
PART b. The Aft Hatch is in a vertical plane with its hinge horizontal at the upper edge and distance S below the surface. Find the torque about the hinge axis, exerted by the sea on the hatch.
PART c. The Forward Hatch is in a vertical plane with the hinge vertical on the left edge. Find the torque about the hinge axis, exerted by the sea.

Attachments

Solution Preview

SEE ATTACHMENT #2 for diagrams showing only hatches, showing dimensions, area elements, moment arms, etc.
Recall that the torque about an axis, exerted by a force, is that force times its moment arm (the perpendicular distance to the axis).

PART a.
Note that since the hatch is horizontal, all parts of it are at the same depth. Therefore, the pressure p, which is a function of depth in a liquid of density D is expressed at depth H by:
(1) p = DgH so the force on any element of area would be the same value, but various area elements are different distances from the hinge axis. The element of torque about the hinge-axis depends on the distance from the axis.
Step 1. Show an element of area, dA, on which the force is dF = p dA, where dA is distance x from the axis. To check your work, SEE ATTACHMENT #2.
Step 2. To express the ...

Solution Summary

Complete with diagrams, the solution carefully explains the step by step computations to arrive at the correct answers.

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