--- title: "Draft tube: purpose, setting and efficiency" subject: "Hydropower Engineering" chapter: 7 key: "semester_7/hydropower_engineering:draft-tube-purpose-setting-equation" source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/draft-tube-purpose-setting-equation site: BCT Engineering --- # Draft tube: purpose, setting and efficiency Hydropower Engineering · Chapter 7: Hydro-electric Machines - Asked in: 2082 Baishakh, 2+3+2 marks - Video: [Draft tube,function of draft tube and types of draft tube](https://www.youtube.com/watch?v=YIEdO63BvgQ) — BEST MECHANICAL ENGINEERING - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/draft-tube-purpose-setting-equation - Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-7 ## Question Why is a draft tube provided at the outlet of a runner of a reaction turbine? Derive the equation for the maximum permissible turbine setting and efficiency of the draft tube. ## Short answer A draft tube recovers runner-exit kinetic energy, allows the turbine above tailwater, and raises effective head. Its efficiency is ηd = [(V1²−V2²)/2g − hf]/(V1²/2g), and maximum setting is Hs,max = Hatm − Hv − ηd V1²/2g, equivalently Hatm − Hv − σcH. ## Answer #### Purpose of a draft tube A draft tube is a gradually expanding pipe connecting the runner outlet to the tailrace. It is provided to: - allow the turbine to be set **above tailwater level** (for easy access) without losing the head between the runner and the tailwater; - **regain kinetic energy** at the runner outlet by reducing the velocity from $V_1$ to $V_2$ and converting it into pressure, thus creating a suction (low pressure) at the runner exit and increasing the effective head; - discharge the water safely into the tailrace. ```text runner outlet (1) | | ^ | | | H_s -----+ +---------- | \ / TWL ~~~~~|~~~~ \/ (2) exit under water ``` #### Maximum permissible setting Let section 1 be the draft tube inlet (runner outlet), at height $H_s$ above tailwater, with velocity $V_1$ and pressure $p_1$. Section 2 is the draft tube outlet submerged in the tailwater, with velocity $V_2$ and pressure $\approx p_{atm}$. Bernoulli's equation between 1 and 2 (datum at tailwater), with loss $h_f$ in the tube: $$ \frac{p_1}{\gamma} + \frac{V_1^2}{2g} + H_s = \frac{p_{atm}}{\gamma} + \frac{V_2^2}{2g} + h_f $$ $$ \frac{p_1}{\gamma} = H_{atm} - H_s - \left[\frac{V_1^2 - V_2^2}{2g} - h_f\right] $$ #### Draft tube efficiency It is the ratio of the kinetic energy actually regained to the kinetic energy at the inlet: $$ \eta_d = \frac{\dfrac{V_1^2 - V_2^2}{2g} - h_f}{\dfrac{V_1^2}{2g}} $$ Substituting in the pressure equation, $$ \frac{p_1}{\gamma} = H_{atm} - H_s - \eta_d\frac{V_1^2}{2g} $$ To avoid cavitation, $p_1 \ge p_v$ (vapour pressure), so $$ H_{s,max} = H_{atm} - H_v - \eta_d\frac{V_1^2}{2g} $$ In terms of the Thoma coefficient $\sigma = \dfrac{H_{atm} - H_v - H_s}{H}$: $$ H_{s,max} = H_{atm} - H_v - \sigma_c H $$ A smaller $\sigma_c$ allows a higher setting. Because the exit velocity head $V_2^2/2g$ and the friction loss $h_f$ are not recovered, $\eta_d$ is less than 1, typically 0.75 to 0.90. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is a draft tube provided? A. To allow setting above tailwater without losing head, recover kinetic energy, and create suction at runner exit B. To increase the water velocity at exit C. To reduce pressure in the penstock D. To store water for peak load Answer: A. Its diverging shape converts velocity head into pressure and lets head be used. (Key point: Purpose) 2. Which expression is draft tube efficiency? A. V2^2/2g divided by V1^2/2g B. [(V1^2 - V2^2)/2g - hf] / (V1^2/2g) C. hf / (V1^2/2g) D. (V1 - V2)/V1 Answer: B. Efficiency is actual regain divided by inlet kinetic head. (Key point: Draft tube efficiency) 3. What is the maximum setting? A. Hs = Hatm + Hv + eta_d V1^2/2g B. Hs = Hatm - eta_d V2^2/2g C. Hs,max = Hatm - Hv - eta_d V1^2/2g D. Hs = Hv - Hatm Answer: C. Setting p1 = pv in the Bernoulli result gives this. (Key point: Setting equation) 4. What does smaller sigma_c allow? A. A lower setting only B. More cavitation C. A larger draft tube angle D. A higher setting above tailwater Answer: D. Hs = Hatm - Hv - sigma_c H increases as sigma_c decreases. 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