Pressure on vertical rectangular plate 2 m × 3 m

For a vertical plane surface: $F = \rho g A \bar h$ and $h^* = \bar h + \dfrac{I_G}{A\bar h}$.

Given: height $d = 2$ m, width $b = 3$ m, top edge 1 m below the surface; water, $\rho = 1000$ kg/m³.

 free surface ===================
           | 1 m
       +---------+  -
       |    G    |  2 m   (b = 3 m)
       |    P    |
       +---------+  -

Data

$$\begin{aligned} A &= 3 \times 2 = 6\ \text{m}^2 \\ \bar h &= 1 + \frac{2}{2} = 2\ \text{m} \\ I_G &= \frac{b d^3}{12} = \frac{3 \times 2^3}{12} = 2\ \text{m}^4 \end{aligned}$$

Total pressure

$$F = 1000 \times 9.81 \times 6 \times 2 = 117\,720\ \text{N} = 117.72\ \text{kN}$$

Centre of pressure

$$\begin{aligned} h^* &= \bar h + \frac{I_G}{A\bar h} = 2 + \frac{2}{6 \times 2} \\ &= 2 + 0.1667 = 2.167\ \text{m} \end{aligned}$$

Answer: $F = 117.72$ kN; centre of pressure is 2.167 m below the free surface (0.167 m below the centroid, on the vertical centre line).