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3
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Homework Solution Manual
Problem 1 Part A:
(4 points for derivation, 0.5 points for the answer and 0.5 points for the units)
The free body diagram for this problem is presented above. In order for the door to swing open
the moment created by the water pressure has to offset the weight moment. Figure above shows
the positive moment (M), x, y, orientations water height (H) and pressure vectors (P) but you can
define these as you want as long as you stay consistent with your definition.
Because the door in this example is rectangular the weight is applied at the centroid and the
moment can be calculated as:
The moment generated by the water pressure is calculated bellow
Setting the weight moment equal to water pressure moment would yield the following
Since the pressure in a static incompressible fluid equals
the height of the water needed to open the door can be computed as:
Part B:
(4 points for derivation, 0.5 points for the answer and 0.5 points for the units)
This is similar to part A but now but because the hinge is replaced by a rail, the door can only
move up/down and the door will open when the force created by the water will offset the door’s
weight.
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 Fall '09

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