---
title: "Max height of straight draft tube (Francis)"
subject: "Hydropower Engineering"
chapter: 7
key: "semester_7/hydropower_engineering:francis-draft-tube-max-height-11760kw"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/francis-draft-tube-max-height-11760kw
site: BCT Engineering
---

# Max height of straight draft tube (Francis)

Hydropower Engineering · Chapter 7: Hydro-electric Machines

- Asked in: 2076 Ashwin, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/francis-draft-tube-max-height-11760kw
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-7

## Question

A Francis turbine works under a head of 25 m and produces 11760 kW while running at 120 rpm. The turbine has been installed at a station where atmospheric pressure is 10 m of water and vapour pressure is 0.20 m of water. Calculate the maximum height of the straight draft tube for the turbine.

## Short answer

Specific speed Ns = 120√11760 / 25^1.25 = 232.8; Thoma coefficient σ = 0.0432(232.8/100)² = 0.234. Maximum draft tube height above tailwater Hs = 10 − 0.20 − 0.234×25 = 3.95 m.

## Answer

#### Data
$H = 25$ m, $P = 11{,}760$ kW, $N = 120$ rpm, $H_{atm} = 10$ m, $H_v = 0.20$ m.

#### Specific speed
$$
N_s = \frac{N\sqrt{P}}{H^{5/4}} = \frac{120\sqrt{11760}}{25^{1.25}} = 232.8
$$

#### Thoma cavitation coefficient
$$
\sigma_c = 0.0432\left(\frac{N_s}{100}\right)^2 = 0.0432 \times (2.328)^2 = 0.2341
$$

#### Maximum height (setting) of the draft tube
The maximum height of the runner outlet / draft tube inlet above the tailwater level is

$$
H_s = H_{atm} - H_v - \sigma_c H = 10 - 0.20 - 0.2341 \times 25 = 3.95\ \text{m}
$$

**Answer: the straight draft tube may be set at most about 3.95 m above the tailwater level (a lower setting is safer).**

## Check yourself

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

1. What is the first step to find the cavitation coefficient?
   A. Compute Hs directly
   B. Compute Ns = N sqrt(Q)/H^(3/4)
   C. Compute Ns = N sqrt(P)/H^(5/4) = 232.8
   D. Compute efficiency
   Answer: C. Ns is needed because sigma_c depends on Ns. (Key point: Specific speed)

2. Which relation gives sigma_c?
   A. sigma_c = (Hatm - Hv)/H
   B. sigma_c = Ns/H
   C. sigma_c = 0.0432 Ns
   D. sigma_c = 0.0432 (Ns/100)^2 = 0.2341
   Answer: D. The empirical relation is sigma_c = 0.0432 (Ns/100)^2. (Key point: Thoma coefficient)

3. What formula gives the maximum height of draft tube inlet above tailwater?
   A. Hs = Hatm - Hv - sigma_c H
   B. Hs = Hatm - sigma_c
   C. Hs = Hatm + Hv + sigma_c H
   D. Hs = sigma_c H
   Answer: A. Hs = 10 - 0.20 - 0.2341 x 25 = 3.95 m. (Key point: Maximum height)

4. How should 3.95 m be interpreted?
   A. The depth below tailwater
   B. The minimum setting
   C. The upper limit above tailwater, with a lower setting being safer
   D. The draft tube length
   Answer: C. It is the maximum permissible height, and lower is safer against cavitation. (Key point: Safety)

## Related in Hydropower Engineering

- [Francis overall efficiency with draft tube](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Afrancis-draft-tube-efficiency-32mw) — Hydropower Engineering, chapter 7
- [Francis runner design (40 m head, 10 m³/s)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Afrancis-turbine-velocity-triangle-40m) — Hydropower Engineering, chapter 7
- [Draft tube: purpose, setting and efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Adraft-tube-purpose-setting-equation) — Hydropower Engineering, chapter 7
- [Francis design (150 m, 25 m³/s)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Afrancis-specific-speed-diameter-setting-150m-25cumec) — Hydropower Engineering, chapter 7, asked 2×
- [Functions of draft tube](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Adraft-tube-functions) — Hydropower Engineering, chapter 7
- [Spiral casing and draft tube location](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aspiral-casing-draft-tube-location) — Hydropower Engineering, chapter 7

## Related in other subjects

- [Why draft tube is used in Francis turbine](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Adraft-tube-francis) — Hydro Power, chapter 7
- [Francis turbine design (55 m³/s, 25 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Afrancis-design-55) — Hydro Power, chapter 7
- [Draft tube functions and inlet pressure](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Adraft-tube-pressure-inlet) — Hydro Power, chapter 7, asked 2×
- [Conical draft tube inlet pressure and efficiency](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aconical-draft-tube-numerical) — Hydro Power, chapter 7