A horizontal rectangular plate of width $0.5\mathrm{m}$ and length $1.2\mathrm{m}$ is fully submerged in water (density $1000kg/{\mathrm{m}}^3$). The upper edge of the plate is $2\mathrm{m}$ below the water surface. What is the hydrostatic force on the plate?

Step-by-step solution

1. Step 1: Compute pressure at upper edge: $p_1=\rho g{h}_1=1000\times 9.8\times 2=19600\mathrm{Pa}$.
2. Step 2: Compute pressure at lower edge: depth $h_2=2+1.2=3.2\mathrm{m}$, $p_2=1000\times 9.8\times 3.2=31360\mathrm{Pa}$.
3. Step 3: Find average pressure on plate: $p_{\text{avg}}=(p_1+p_2)/2=(19600+31360)/2=25480\mathrm{Pa}$.
4. Step 4: Calculate area of plate: $A=0.5\times 1.2=0.6{\mathrm{m}}^2$.
5. Step 5: Compute hydrostatic force: $F=p_{\text{avg}}\times A=25480\times 0.6=15288\mathrm{N}$.
6. Step 6: Conclude the force is $15288\mathrm{N}$.

Concept tested: Hydrostatic force on horizontal plate

Published 7 October 2026 · How this solution was prepared and checked