Answer: F = 211312.5ft/lb.
Step-by-step explanation: Hydrostatic pressure is pressure caused by a fluid due to the force of gravity. It is calculated following the formula:
P = ρgh.
ρ is the fluid density (62.5 lb/ft³);
g is the gravitacional acceleration( 32.2ft/s²);
h is the height of the fluid columm;
P = 62.5.32.2.h
Pressure at h = 1ft:
P = 62.5.32.2.1
P = 2012.5 psi.
Now, hydrostatic force is F = [tex]\frac{P}{A}[/tex]
The pressure exerted on the surface is not constant. It depends on the height. So, to evaluate the force:
dF = P(h) dA
Since it a rectangular plate, dA = w.dh, where w is its width and equals 6 and dh is its height element.
That gives: dF = P(h)w.dh
[tex]\int\limits^a_b {2012.5hw} \, dh[/tex] = 2012.5.6. [tex]\int\limits^6_1 {h} \, dh[/tex] = 2012.5.6([tex]\frac{h^{2} }{2}[/tex]) = 12075([tex]\frac{6^{2} }{2} - \frac{1^{2} }{2}[/tex]) = 211312.5ft/lb.
