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# Solving for Volume Using Multiple Integration

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This is a past exam question.
Please help me understand how to go about questions a and b. I think I need some kind of double integral or something?

Systems Engineering B

The shape of the hull of a small barge of width w, length l and depth d, can be approximated by the multivariable function f(x,y), where:

(a) Show via multiple integration that the volume V of the hull is given by the following expression:

(b) If the mass of the barge is 100 tonnes, and its sides must clear the water by at least 1 m to safeguard against sinking, what is the maximum payload of the vessel, to the nearest 100 tonnes?

Vessel dimensions: w=6m
l=20m
d=9m

https://brainmass.com/physics/fluid-dynamics/solving-volume-multiple-integration-2010

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Solution attached.

Systems Engineering B

The shape of the hull of a small barge of width w, length l and depth d, can be approximated by the multivariable ...

#### Solution Summary

This solution provides a detailed explanation of how to solve a fluid mechanics problem based on proving that certain expressions represent the measurements of the hull of a small barge. A step-by-step explanation is provided to illustrate the solutions for both parts of this question. In order to view the full the solution, a Word Document attachment must be opened.

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