Question

A square plate with sides a is submerged vertically in water as shown. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Use delta for δ, the weight density constant.)

Answer 1

if you still need help on this, pls let me know. i can come back later today and post something. the trick, in simple x-y space, is to integrate P(y) = P - ∂gh along the edges modelled as y = x and y = -x (Bernoulli pressure wrt surface and i would give it unit depth just to keep it real in the physical sense).

i would do that wrt ds (the arc length * unti width and post the answers in simple vectors, if that makes sense. little bit fiddly but very do-able.