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Surge tank functions and formulas

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)).

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.

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)

LL = tunnel length, AtA_t = tunnel area, AsA_s = surge tank area, V0V_0 = initial velocity in the tunnel, gg = gravity, hfh_f = friction loss at V0V_0 (hf=αV02h_f=\alpha V_0^2), H0H_0 = gross head.

QuantityFormula
Max upsurge (full rejection, no friction)Zmax=V0L Atg AsZ_{max}=V_0\sqrt{\dfrac{L\,A_t}{g\,A_s}}
Max downsurge (sudden demand, no friction)Zmin=−ΔVL Atg AsZ_{min}=-\Delta V\sqrt{\dfrac{L\,A_t}{g\,A_s}}
Effect of frictionFriction 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∗=hfV0gAsLAtZ^*=\dfrac{h_f}{V_0}\sqrt{\dfrac{gA_s}{LA_t}}
Time period of oscillationT=2πL Asg AtT=2\pi\sqrt{\dfrac{L\,A_s}{g\,A_t}}
Minimum area (Thoma stability)Ath=L At2g α (H0−hf)A_{th}=\dfrac{L\,A_t}{2g\,\alpha\,(H_0-h_f)}

where α=hfV02\alpha=\dfrac{h_f}{V_0^2}. For a partial change of discharge, V0V_0 is replaced by the change ΔV\Delta V in the tunnel velocity. The area of the tank is taken as 1.0-1.5 times AthA_{th} (usually larger when the upsurge/downsurge governs the design).

✓ Answer checked by Claude Opus 5.5 (high effort)

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