Water hammer and how to minimize it

Water hammer is the sudden rise (or fall) of pressure in a penstock when the velocity of water is changed quickly, for example when the turbine gates close quickly after a load rejection. The moving column of water is suddenly stopped; its kinetic energy is converted into pressure energy, and a pressure wave travels up and down the pipe with a hammering effect.

Magnitude (Joukowsky relation): for instantaneous or rapid closure ($t_c \le 2L/a$),

$$\Delta p = \rho\, a\, \Delta v \quad\text{or}\quad \Delta H = \frac{a\,\Delta v}{g}$$

where $a$ = speed of the pressure wave in the pipe (about 1000–1400 m/s), $\Delta v$ = change in velocity, $L$ = pipe length. For slow (gradual) closure ($t_c > 2L/a$) the rise is smaller. Rigid-column theory gives $\Delta p \approx \rho L \Delta v / t_c$; Michaud's formula, which allows for the reflected pressure wave, gives about $2\rho L \Delta v / t_c$.

 Reservoir
 ~~~~~~~ |
         |\  penstock (length L)
         | \
         |  \  pressure wave
         |   \  <---->
         |    \______[gate]--turbine
                      closes

Effects: very high pressure can burst the penstock and damage valves and the turbine casing; negative pressure on opening can collapse the pipe or cause cavitation; it causes vibration and noise; and it makes speed governing more difficult.

Methods to minimize water hammer

1. Surge tank near the power house: gives a free water surface close to the turbine, so the length of pipe in which water hammer occurs is reduced and the pressure wave is reflected from the tank.
2. Slow closure of gates: make the closing time longer than $2L/a$ (governor relief/time setting).
3. Relief valve / pressure relief valve on the penstock or casing, which opens when the pressure rises and lets water escape.
4. Jet deflector (Pelton turbines): the jet is deflected away from the buckets at once, while the needle closes slowly.
5. Bypass / synchronous bypass valve, which opens as the gate closes so that the penstock flow does not stop suddenly.
6. Strong penstock designed for the expected surge pressure, and air valves to prevent vacuum collapse.
7. Keep the penstock as short as possible and the water velocity low (larger diameter).