Question: A swimming pool filled with liquid of density has a set of n steps at

Question

Question:  A swimming pool filled with liquid of density has a set of n steps at one end.  Each step has a horizontal and vertical length of h/n where h is the total depth.  The width of the steps out of the page is 6h.  Compute the hydrostatic force on the set of steps.

Provided with this as a hint:

My thought on how to solve this is to simply calculate the pressure for each step and sum.  Is this correct?  How does the "hint" above come into play?  I'd assume with an integral of some sort, but not sure how to set it up.

Explanation / Answer

from the question it is clear that the area of each step is a = [6h]*[h/n] now if go for finding the Force on each step, it is the product of are and the pressure on each step
obviously the pressure on the top step is less when compared to the pressure that acts on last step hence if the pressure is looked upon we can get a relation that looks some what like this

Force on first step = g(h/n) * [6h] * [h/n]

Force on second step = 2 * g(h/n) * [6h] * [h/n]

Force on third step = 3 * g(h/n) * [6h] * [h/n]

;

;

;

Force on last step = n * g(h/n) * [6h] * [h/n]

total force on steps = from(i=1 to n) i * g(h/n) * [6h] * [h/n] = g(h/n) * [6h] * [h/n] * (n)(n+1)/2

total force on steps = 3 g(h^3)(n+1)/n

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