--- title: "Surge tank functions and formulas" subject: "Hydropower Engineering" chapter: 6 key: "semester_7/hydropower_engineering:surge-tank-functions-formulas" source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/surge-tank-functions-formulas site: BCT Engineering --- # Surge tank functions and formulas Hydropower Engineering · Chapter 6: Water Conveyance Structures - Asked in: 2075 Chaitra, 6 marks - Video: [What is Surge Tank : Concept and Solved Numerical Problem](https://www.youtube.com/watch?v=vynh15jkI5k) — Hydropower - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/surge-tank-functions-formulas - Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-6 ## Question What are the functions of a surge tank? Write down the formulas to calculate the maximum upsurge and downsurge, time of oscillation and minimum area of a surge tank with usual notations. ## Short answer A surge tank reduces water hammer, acts as a reservoir for sudden flow changes, protects the tunnel and penstock, and improves governor stability. Max upsurge Zmax = V0 sqrt(L At/(g As)), max downsurge Zmin = -ΔV sqrt(L At/(g As)), oscillation period T = 2π sqrt(L As/(g At)), minimum area Ath = L At/(2g α (H0 - hf)). ## Answer #### Functions of a surge tank 1. **Reduces water hammer**: it reflects the pressure waves, so the long headrace tunnel is protected from high pressure rise or fall. 2. **Acts as a reservoir** that supplies the extra water when the turbine discharge is suddenly increased, and absorbs the water when the discharge is suddenly cut off. 3. Protects the tunnel from collapse and the penstock from over-pressure; reduces the length of the pipe in which the water hammer acts. 4. Improves **speed regulation** of the turbine (governor stability) by letting the tunnel flow change slowly. #### Formulas (simple cylindrical tank, usual notations) $L$ = tunnel length, $A_t$ = tunnel area, $A_s$ = surge tank area, $V_0$ = initial velocity in the tunnel, $g$ = gravity, $h_f$ = friction loss at $V_0$ ($h_f=\alpha V_0^2$), $H_0$ = gross head. | Quantity | Formula | |---|---| | Max upsurge (full rejection, no friction) | $Z_{max}=V_0\sqrt{\dfrac{L\,A_t}{g\,A_s}}$ | | Max downsurge (sudden demand, no friction) | $Z_{min}=-\Delta V\sqrt{\dfrac{L\,A_t}{g\,A_s}}$ | | Effect of friction | Friction damps the oscillation, so the upsurge and downsurge are smaller than these frictionless values; exact values are read from Jaeger's/Johnson's charts in terms of $Z^*=\dfrac{h_f}{V_0}\sqrt{\dfrac{gA_s}{LA_t}}$ | | Time period of oscillation | $T=2\pi\sqrt{\dfrac{L\,A_s}{g\,A_t}}$ | | Minimum area (Thoma stability) | $A_{th}=\dfrac{L\,A_t}{2g\,\alpha\,(H_0-h_f)}$ | where $\alpha=\dfrac{h_f}{V_0^2}$. For a partial change of discharge, $V_0$ is replaced by the change $\Delta V$ in the tunnel velocity. The area of the tank is taken as 1.0-1.5 times $A_{th}$ (usually larger when the upsurge/downsurge governs the design). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is a function of a surge tank? A. Removes sediment B. Generates power C. Raises head D. Reflects pressure waves to reduce water hammer and acts as a reservoir on load change Answer: D. It protects the tunnel and supplies or absorbs water on sudden load change. (Key point: Function) 2. What is the frictionless max upsurge on full rejection? A. Z = 2 pi sqrt(L A_s/(g A_t)) B. Z = V0^2/2g C. Z = V0 sqrt(g A_s/(L A_t)) D. Z = V0 sqrt(L A_t/(g A_s)) Answer: D. Derived from SHM: amplitude V0 sqrt(L At/(g As)). (Key point: Upsurge formula) 3. The period of oscillation is? A. T = sqrt(L/g) B. T = 2 pi sqrt(L A_s/(g A_t)) C. T = 2 pi sqrt(L A_t/(g A_s)) D. T = L/V0 Answer: B. omega = sqrt(g At/(L As)) so T = 2 pi/omega. (Key point: Period) 4. How does friction change the surge values? A. No effect B. Doubles the period C. Damps oscillation, so surges are smaller than frictionless D. Increases the surges Answer: C. Friction dissipates energy; exact values come from charts. (Key point: Friction effect) 5. Minimum area for stability is? A. L A_t g alpha B. V0^2/(2 g) C. 2 g L/(A_t) D. L A_t/(2 g alpha (H0 - hf)) Answer: D. With alpha = hf/V0^2; actual area taken 1.0-1.5 times A_th. 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