---
title: "Pressure on circular plate (2.6 m)"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:circular-plate-2-6m"
source: https://www.bctengineer.com/q/semester_6/hydro_power/circular-plate-2-6m
site: BCT Engineering
---

# Pressure on circular plate (2.6 m)

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

- Asked in: 2079 Chaitra, 5 marks
- Video: [Problem on Vertical Circular Plate Immersed in Water - Fluid Mechanics 1](https://www.youtube.com/watch?v=vJcFaNG9QPA) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/circular-plate-2-6m
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

A circular plate 2.6 m in diameter is immersed in water, its greatest and least depth below the free surface being 3 m and 1 m respectively. Find the total pressure on one face of the plate and the position of the center of pressure.

## Short answer

The inclined circular plate (diameter 2.6 m) has total pressure 104.17 kN using F = ρgA h̄ with centroid depth 2 m. Center of pressure is at 2.125 m depth from h* = h̄ + (IG sin²θ)/(A h̄).

## Answer

The plate is not vertical because its depth range (3 − 1 = 2 m) is less than its diameter, so it is inclined. Use the formulas for an inclined plane surface.

**Given:** $d = 2.6$ m, water, $\rho = 1000$ kg/m³, depths of top and bottom points $= 1$ m and $3$ m.

```text
  free surface =====================
         :  1 m
         :     * top point
         :    / \
         :   /   \   plate, d = 2.6 m
         :  /  G  \   inclined at theta
         :   \   /
         :    \ /
         :     * bottom point (3 m)
```

#### Inclination and centroid depth
$$
\begin{aligned}
\sin\theta &= \frac{3 - 1}{2.6} = 0.7692 \\
\bar h &= \frac{1 + 3}{2} = 2\ \text{m}
\end{aligned}
$$

#### Area and second moment of area
$$
\begin{aligned}
A &= \frac{\pi}{4}(2.6)^2 = 5.3093\ \text{m}^2 \\
I_G &= \frac{\pi d^4}{64} = \frac{\pi (2.6)^4}{64} = 2.2432\ \text{m}^4
\end{aligned}
$$

#### Total pressure
$$
\begin{aligned}
F &= \rho g A \bar h = 1000 \times 9.81 \times 5.3093 \times 2 \\
&= 104\,168\ \text{N} = 104.17\ \text{kN}
\end{aligned}
$$

#### Centre of pressure
$$
\begin{aligned}
h^* &= \bar h + \frac{I_G \sin^2\theta}{A \bar h} \\
&= 2 + \frac{2.2432 \times 0.5917}{5.3093 \times 2} \\
&= 2 + 0.1250 = 2.125\ \text{m}
\end{aligned}
$$

**Answer:** total pressure $F \approx 104.17$ kN; centre of pressure at a depth of $2.125$ m below the free surface (on the plate's vertical diameter, below the centroid).

## Check yourself

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

1. For the 2.6 m diameter plate with depths 1 m and 3 m, how do we know it is inclined and find its angle?
   A. Depth range is greater than the diameter; theta = 0
   B. Depth range 2 m is less than 2.6 m; sin(theta) = 2/2.6
   C. Depth range 2 m equals the diameter; theta = 90 deg
   D. Water density is 1000 so it must be inclined
   Answer: B. Vertical depth difference over the diameter gives sin(theta) = 2/2.6 = 0.7692. (Key point: Detecting inclination)

2. Which second moment of area about the centroidal axis is used for the circular plate?
   A. b d^3 / 12
   B. pi d^3 / 32
   C. pi d^4 / 64
   D. pi d^2 / 4
   Answer: C. I_G = pi d^4 / 64 for a circle, giving 2.2432 m^4 for d = 2.6 m. (Key point: Second moment of a circle)

3. What is the total pressure on one face in water (centroid depth 2 m, A = 5.3093 m^2)?
   A. About 104.17 kN
   B. About 208.3 kN
   C. About 156.3 kN
   D. About 52.1 kN
   Answer: A. F = 1000 x 9.81 x 5.3093 x 2 = 104.17 kN. (Key point: Total pressure)

4. Where does the centre of pressure lie relative to the centroid?
   A. At the bottom point, 3 m depth
   B. Above the centroid
   C. Below the centroid, at 2.125 m depth
   D. At the centroid
   Answer: C. The correction term I_G sin^2(theta)/(A h_bar) is positive (0.125 m), so the centre of pressure is below the centroid. (Key point: Centre of pressure position)

## Close variants set in other exams

- [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×

## Related in Hydro Power

- [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
- [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 vertical rectangular plate 2 m × 3 m](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Arectangular-plate-2x3) — Hydro Power, chapter 1
- [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

## Related in other subjects

- [Total pressure and centre on tank face AB](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aoil-tank-pressure-on-ab) — Fluid Mechanics, chapter 3
- [RoR layout: pressure tunnel and free surface](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aror-layout-pressure-tunnel-free-flow) — Hydropower Engineering, chapter 2
- [One cycle of water hammer pressure wave](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awater-hammer-one-cycle-wave-sketch) — Hydraulics, chapter 4, asked 2×
- [Boussinesq stress below circle center](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aboussinesq-circle-center-stress) — Soil Mechanics, chapter 8