Ariver barge, whose cross section is approximately rectangular, carries a load of grain. the barge is 28 ft wide and 93 ft long. when unloaded its draft (depth of submergence) is 6 ft, and with the load of grain the draft is 9 ft. determine: (a) the unloaded weight of the barge, and (b) the weight of the grain.

a)

b)

Explanation:

Part a

For this case we have the situation illustrated on Figure 1.  We will have two forces involved in equilibrium the weight and the Bouyance force, and since the system is on equilibrium we have:

So then we have:

Where represent the submerged volume. represent the specific weight for the fluid. So we can replace and we have:

Part b

As we can see on figure 2 attached we have the illustration for this case. We add the weight for the grain and now the depth is 9ft.

W can do the balance of forces in the vertical and we got again:

Where represent the weight for the grain.

And if we solve for we got:

Where represent the specific weight of rthe water and the submerged volume. If we replace we got:

it may be wrong but i think its a