---
title: "Pressure on vertical rectangular plate 2 m × 3 m"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:rectangular-plate-2x3"
source: https://www.bctengineer.com/q/semester_6/hydro_power/rectangular-plate-2x3
site: BCT Engineering
---

# Pressure on vertical rectangular plate 2 m × 3 m

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2081 Asoj, 5 marks
- Video: [Solved Example: Hydrostatic Forces on a Vertical Gate](https://www.youtube.com/watch?v=JdeXZ3k2Y9U) — Fluid Matters
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/rectangular-plate-2x3
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Calculate the total pressure and center of pressure on a vertically submerged rectangular plate 2 m high and 3 m wide, with the top edge 1 m below the free surface.

## Short answer

Vertical rectangular plate (2 m × 3 m) with top edge 1 m below surface gives total pressure 117.72 kN from F = ρgA h̄ (h̄ = 2 m). Center of pressure is at 2.167 m depth using h* = h̄ + IG/(A h̄).

## Answer

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.

```text
 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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For a vertical 2 m high plate with its top edge 1 m below the surface, what is the centroid depth?
   A. 2 m
   B. 3 m
   C. 1 m
   D. 1.5 m
   Answer: A. h_bar = 1 + 2/2 = 2 m. (Key point: Centroid depth)

2. Which I_G is used for the vertical rectangle of width b = 3 m and height d = 2 m?
   A. d b^3/12 = 4.5 m^4
   B. b d^3/3 = 8 m^4
   C. b d^2/2 = 6 m^4
   D. b d^3/12 = 2 m^4
   Answer: D. For a vertical rectangle I_G = b d^3 / 12 with d the vertical height: 3 x 8 / 12 = 2 m^4. (Key point: Second moment of rectangle)

3. What is the total pressure on the plate?
   A. 235.44 kN
   B. 58.86 kN
   C. 117.72 kN
   D. 176.58 kN
   Answer: C. F = rho g A h_bar = 1000 x 9.81 x 6 x 2 = 117.72 kN. (Key point: Total pressure)

4. What is the depth of the centre of pressure?
   A. 2.500 m
   B. 2.000 m
   C. 2.333 m
   D. 2.167 m
   Answer: D. h* = 2 + I_G/(A h_bar) = 2 + 2/12 = 2.167 m, 0.167 m below the centroid. (Key point: Centre of pressure)

## Related in Hydro Power

- [Pressure on inclined rectangular plate](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ainclined-rectangular-plate) — Hydro Power, chapter 1
- [Pressure on rectangular plate 3 m × 5 m](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Arectangular-plate-3x5) — Hydro Power, chapter 1
- [Centre of pressure below centroid proof](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Acentre-pressure-below-centroid) — Hydro Power, chapter 1
- [Pressure on circular plate (2.2 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Acircular-plate-2-2m) — Hydro Power, chapter 1
- [Pressure on isosceles triangular plate](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-plate-pressure) — Hydro Power, chapter 1
- [Pressure on circular plate (2.5 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Acircular-plate-2-5m) — Hydro Power, chapter 1, asked 2×

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