---
title: "Hydrostatic thrust and uplift with drainage gallery"
subject: "Hydro Power"
chapter: 4
key: "semester_6/hydro_power:dam-thrust-uplift-gallery"
source: https://www.bctengineer.com/q/semester_6/hydro_power/dam-thrust-uplift-gallery
site: BCT Engineering
---

# Hydrostatic thrust and uplift with drainage gallery

Hydro Power · Chapter 4: Dam Engineering

- Asked in: 2074 Bhadra, 5+5 marks
- Video: [[ADI] FORCES ACTING ON GRAVITY DAM!!! (CE) In Hindi](https://www.youtube.com/watch?v=96JBR5hZLaI) — ADI ThE ScIeNcE GuY
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/dam-thrust-uplift-gallery
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-4

## Question

A concrete gravity dam has maximum reservoir level 250 m, base level of dam 200 m, tail water elevation 210 m, base width of dam 40 m, location of drainage gallery 10 m from upstream face which may be assumed as vertical. Compute hydrostatic thrust and uplift force per unit length of dam at its base level. Assume 50% reduction in net seepage head at the location of the drainage gallery.

## Short answer

Net hydrostatic thrust: 11,772 kN/m (upstream 12,262.5, tailwater 490.5). Uplift force: 9,810 kN/m, acting 15.33 m from the heel.

## Answer

#### Data
- Upstream water depth $h_1 = 250 - 200 = 50$ m; tailwater depth $h_2 = 210 - 200 = 10$ m.
- Base width $B = 40$ m; drainage gallery 10 m from the vertical upstream face. $\gamma_w = 9.81$ kN/m³. Values are per metre length of dam.

#### Hydrostatic thrust

$$
\begin{aligned}
P_1 &= \frac{1}{2}\gamma_w h_1^2 = \frac{1}{2}\times9.81\times50^2 = 12{,}262.5\ \text{kN} \ (\text{at } 16.67\ \text{m above base}) \\
P_2 &= \frac{1}{2}\gamma_w h_2^2 = \frac{1}{2}\times9.81\times10^2 = 490.5\ \text{kN} \ (\text{at } 3.33\ \text{m above base}) \\
P_{net} &= 12{,}262.5 - 490.5 = 11{,}772\ \text{kN}\ (\text{downstream})
\end{aligned}
$$

#### Uplift pressure
Net seepage head $= h_1 - h_2 = 40$ m. It is reduced by 50% at the gallery:

$$
h_g = h_2 + 0.5(h_1 - h_2) = 10 + 20 = 30\ \text{m}
$$

| Point | Head (m) | Pressure (kN/m²) |
|---|---|---|
| Heel | 50 | 490.5 |
| Gallery (10 m) | 30 | 294.3 |
| Toe | 10 | 98.1 |

```text
 heel      gallery              toe
  |<- 10 ->|<------- 30 -------->|
  |\       |                     |
  | \      |                     |
  |  \_____|_____________        |
  |        |             -----___|
  | 490.5  | 294.3          98.1 |
```

$$
\begin{aligned}
U_1 &= \frac{490.5 + 294.3}{2} \times 10 = 3{,}924\ \text{kN} \\
U_2 &= \frac{294.3 + 98.1}{2} \times 30 = 5{,}886\ \text{kN} \\
U &= 3{,}924 + 5{,}886 = 9{,}810\ \text{kN}
\end{aligned}
$$

Its line of action (moments about heel) is at 15.33 m from the heel.

For comparison, without the gallery: $U = \frac{490.5 + 98.1}{2}\times40 = 11{,}772$ kN, so the gallery reduces uplift by about 17%.

**Answer: Net hydrostatic thrust = 11,772 kN/m (upstream 12,262.5 kN/m, tailwater 490.5 kN/m); uplift force = 9,810 kN/m acting 15.33 m from the heel.**

## Check yourself

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

1. Upstream 12,262.5 kN and tailwater 490.5 kN. What is the net hydrostatic thrust?
   A. 11,772 kN downstream
   B. 490.5 kN
   C. 12,262.5 kN
   D. 12,753 kN
   Answer: A. Tailwater pressure acts upstream, so net thrust = 12,262.5 - 490.5 = 11,772 kN. (Key point: Net thrust)

2. 50% reduction in the net seepage head (h1 - h2 = 40 m) at the gallery gives what head there?
   A. 20 m
   B. 30 m, i.e. h2 + 0.5(h1 - h2)
   C. 25 m
   D. 10 m
   Answer: B. The reduced head is added to tailwater head: 10 + 20 = 30 m, pressure 294.3 kN/m2. (Key point: Head at gallery)

3. Total uplift with the gallery?
   A. 11,772 kN
   B. 15,696 kN
   C. 9,810 kN, from 3,924 + 5,886
   D. 3,924 kN
   Answer: C. The two trapezoids give 3,924 and 5,886 kN; without the gallery U = 11,772 kN. (Key point: Uplift force)

## Related in Hydro Power

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## Related in other subjects

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- [Gravity dam concrete volume from hydrostatic thrust](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-width-hydrostatic-thrust) — Hydropower Engineering, chapter 4
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- [Uplift pressure diagram with drainage gallery](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Auplift-pressure-diagram-gravity-dam) — Hydropower Engineering, chapter 4