---
title: "Uplift force with and without drainage gallery"
subject: "Hydro Power"
chapter: 4
key: "semester_6/hydro_power:uplift-force-drainage-gallery"
source: https://www.bctengineer.com/q/semester_6/hydro_power/uplift-force-drainage-gallery
site: BCT Engineering
---

# Uplift force with and without drainage gallery

Hydro Power · Chapter 4: Dam Engineering

- Asked in: 2070 Bhadra, 3+3 marks
- Video: [Uplift pressure diagram with Numerical](https://www.youtube.com/watch?v=juVB4KNRLHc) — Civil Engineering Studies
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/uplift-force-drainage-gallery
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-4

## Question

Determine the uplift pressure force on a gravity dam of 40 m height, 10 m top width with u/s face vertical and the base width = 30 m. The tail water depth is 5 m and the free board is 3 m. What will be the uplift pressure force when there is a drainage gallery at a distance of 6 m from u/s face?

## Short answer

Uplift pressure varies linearly from heel to toe. Without drainage, uplift force = 6,180.3 kN/m. With gallery 6 m from heel, head at drain = tailwater + 1/3 difference, uplift force = 3,982.9 kN/m.

## Answer

#### Data (per metre length)
- Dam height 40 m, free board 3 m, so upstream water depth $h_1 = 37$ m.
- Tailwater depth $h_2 = 5$ m, base width $B = 30$ m, $\gamma_w = 9.81$ kN/m³.
- Full uplift is assumed (C = 1): pressure varies linearly from $\gamma_w h_1$ at the heel to $\gamma_w h_2$ at the toe.

#### (a) Without drainage gallery

Heel: $9.81 \times 37 = 362.97$ kN/m²; toe: $9.81 \times 5 = 49.05$ kN/m².

$$
U = \frac{362.97 + 49.05}{2} \times 30 = 6{,}180.3\ \text{kN/m}
$$

#### (b) With drainage gallery 6 m from upstream face
By the usual rule (IS 6512), the uplift head at the line of drains is the tailwater head plus one-third of the difference:

$$
h_d = h_2 + \frac{1}{3}(h_1 - h_2) = 5 + \frac{32}{3} = 15.67\ \text{m} \Rightarrow p_d = 153.69\ \text{kN/m}^2
$$

```text
heel  drain                    toe
 |<-6->|<-------- 24 --------->|
 |\    |                       |
 | \   |                       |
 |  \__|______                 |
 |     |      -------______    |
362.97 153.69             49.05
```

$$
\begin{aligned}
U_1 &= \frac{362.97 + 153.69}{2} \times 6 = 1{,}550.0\ \text{kN/m} \\
U_2 &= \frac{153.69 + 49.05}{2} \times 24 = 2{,}432.9\ \text{kN/m} \\
U &= 1{,}550.0 + 2{,}432.9 = 3{,}982.9\ \text{kN/m}
\end{aligned}
$$

**Answer: Uplift force = 6,180.3 kN per metre without drains; 3,982.9 kN per metre with the drainage gallery at 6 m.** The gallery cuts uplift by about 36%.

## Check yourself

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

1. Dam 40 m high, freeboard 3 m. What is the upstream water depth?
   A. 37 m
   B. 43 m
   C. 35 m
   D. 40 m
   Answer: A. h1 = 40 - 3 = 37 m. (Key point: Water depth)

2. How is the uplift computed without a gallery?
   A. Triangular from heel to zero at toe
   B. Linear (trapezoidal) from gamma_w h1 at heel to gamma_w h2 at toe, giving 6,180.3 kN/m
   C. Zero
   D. Uniform at 362.97 kN/m2
   Answer: B. U = (362.97 + 49.05)/2 x 30 = 6,180.3 kN. (Key point: Without gallery)

3. Head at drain line at 6 m from the u/s face?
   A. 5 m
   B. 37 m
   C. 15.67 m = 5 + 32/3
   D. 21 m
   Answer: C. h2 + (h1 - h2)/3 = 15.67 m, giving uplift 3,982.9 kN, about 36% lower. (Key point: With gallery)

## Related in Hydro Power

- [Hydrostatic thrust and uplift with drainage gallery](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Adam-thrust-uplift-gallery) — Hydro Power, chapter 4
- [Elementary profile and 40 m gravity dam stability](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-elementary-40m) — Hydro Power, chapter 4
- [Stability of gravity dam (crest 1530 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-stability-1530) — Hydro Power, chapter 4
- [Stability of trapezoidal gravity dam (RL 250 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atrapezoidal-dam-stability-250m) — Hydro Power, chapter 4
- [Sliding and overturning check of gravity dam](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-sliding-overturning-figure) — Hydro Power, chapter 4
- [Stresses in gravity dam with drain holes](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-stresses-figure) — Hydro Power, chapter 4

## Related in other subjects

- [Gravity dam stresses with drainage gallery uplift](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stresses-2080-baishakh) — Hydropower Engineering, chapter 4
- [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
- [Base width of 20 m high trapezoidal gravity dam](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-base-width-trapezoidal-20m) — Hydropower Engineering, chapter 4
- [Gravity dam forces and stability checks (2081 Baishakh)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-forces-stresses-2081-baishakh) — Hydropower Engineering, chapter 4