---
title: "Khosla: average hydraulic gradient, uplift A-D"
subject: "Irrigation and Drainage Engineering"
chapter: 5
key: "semester_6/irrigation_and_drainage_engineering:khosla-average-gradient-uplift-abcd-g224"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-average-gradient-uplift-abcd-g224
site: BCT Engineering
---

# Khosla: average hydraulic gradient, uplift A-D

Irrigation and Drainage Engineering · Chapter 5: Diversion Headworks

- Asked in: 2072 Magh, 6 marks
- Video: [Khosla's Theory of Design of Weirs | Irrigation - GATE](https://www.youtube.com/watch?v=ooZ7Lv3WRLc) — Ekeeda GATE & ESE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-average-gradient-uplift-abcd-g224
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-5

## Question

A section of a hydraulic structure is shown in figure below, calculate the average hydraulic gradient. Also find the uplift pressures at points A, B, C, and D. Find the thickness of the floor at these points. Take G = 2.24.

[Figure: head of 5 m; pile depths 8 m and 10 m; points A, B, C, D at distances of 10 m, 15 m, 20 m, 25 m and total 30 m from the upstream end]

## Short answer

Bligh's creep length is 66 m, so average hydraulic gradient is 5/66 = 0.0758 (1 in 13.2). Uplift heads at A, B, C, D are 3.03, 2.65, 2.27, 1.89 m; pressures 29.7, 26.0, 22.3, 18.6 kN/m². Required floor thickness with G=2.24 and 33% safety is 3.26, 2.85, 2.44, 2.04 m.

## Answer

The figure is read as an impervious floor of length 30 m with a cut-off pile of depth 8 m at the upstream end and 10 m at the downstream end, under a head $H = 5$ m. Points A, B, C, D lie on the floor at 10, 15, 20 and 25 m from the upstream end. The creep (seepage) path is found first, then Bligh's linear loss of head is used.

#### Creep length and average hydraulic gradient
The water creeps down the upstream pile, along the floor and up the downstream pile.

$$
\begin{aligned} L &= 2d_1 + b + 2d_2 = 2(8) + 30 + 2(10) = 66\ \text{m} \\ i_{avg} &= \frac{H}{L} = \frac{5}{66} = 0.0758 \approx \frac{1}{13.2} \end{aligned}
$$

#### Uplift pressure at A, B, C, D
Head lost up to a point $= i_{avg}\times$ (creep length to the point). The upstream pile adds $2\times 8 = 16$ m before the floor starts. Residual (uplift) head $h = H - \text{head lost}$ and pressure $p = \gamma_w h$ with $\gamma_w = 9.81$ kN/m³.

| Point | Distance from u/s end (m) | Creep length to point (m) | Head lost (m) | Residual head $h$ (m) | Uplift (kN/m²) | Floor thickness $t$ (m) |
|---|---|---|---|---|---|---|
| A | 10 | 26 | 1.97 | 3.03 | 29.7 | 3.26 |
| B | 15 | 31 | 2.35 | 2.65 | 26.0 | 2.85 |
| C | 20 | 36 | 2.73 | 2.27 | 22.3 | 2.44 |
| D | 25 | 41 | 3.11 | 1.89 | 18.6 | 2.04 |

#### Thickness of floor
Bligh's rule, with an extra 33 % for safety, for specific gravity $G = 2.24$:

$$
t = \frac{4}{3}\,\frac{h}{G-1} = \frac{4}{3}\,\frac{h}{1.24}
$$

For example at A: $t = \frac{4}{3}\times\frac{3.03}{1.24} = 3.26$ m.

**Answer:** average gradient $= 0.0758$ (1 in 13.2). Uplift heads at A, B, C, D $= 3.03$, 2.65, 2.27, 1.89 m of water (i.e. 29.7, 26.0, 22.3, 18.6 kN/m²). Floor thickness $= 3.26$, 2.85, 2.44, 2.04 m respectively.

## Check yourself

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

1. For piles 8 m and 10 m and floor 30 m, the total creep length is
   A. 66 m
   B. 30 m
   C. 38 m
   D. 48 m
   Answer: A. L = 2(8) + 30 + 2(10) = 66 m. (Key point: Creep length)

2. With H = 5 m and L = 66 m, the average gradient is
   A. 0.167
   B. 0.132
   C. 0.0303
   D. 0.0758 (about 1 in 13.2)
   Answer: D. i = H/L = 5/66 = 0.0758. (Key point: Average gradient)

3. Creep length to A is 26 m (16 m of u/s pile plus 10 m of floor). Head lost is
   A. 1.97 m
   B. 0.76 m
   C. 5 m
   D. 3.03 m
   Answer: A. Head lost = 0.0758 x 26 = 1.97 m, leaving residual head 3.03 m. (Key point: Head lost at A)

4. Which formula gives the floor thickness here with G = 2.24?
   A. t = (3/4) h/(G-1)
   B. t = (4/3) h/(G-1)
   C. t = h/G
   D. t = h/(G+1)
   Answer: B. Bligh's rule with an extra 33% for safety: t = (4/3)(3.03)/1.24 = 3.26 m at A. (Key point: Floor thickness with extra safety)

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