Hydrostatic Pressure and Force — Question 5

Question 5 – Solution

Step 1: Use the centroid formula. For any vertical plane region submerged in a liquid of constant weight density, $$F=\gamma A\bar y.$$

Step 2: Write the force on each plate. Let the common area be $A$. If Plate 1 has centroid depth $3$ m and Plate 2 has centroid depth $5$ m, then $$F_1=\gamma A(3),\qquad F_2=\gamma A(5).$$

Step 3: Compare the forces. $$\frac{F_2}{F_1} =\frac{\gamma A(5)}{\gamma A(3)} =\frac53.$$ The shape does not affect this comparison because both plates have the same area; only the centroid depth differs. $$\boxed{F_2=\frac53F_1}$$ Thus the deeper plate experiences $66\tfrac23\%$ more force.