Forebay design procedure

A forebay is a small reservoir at the end of the headrace (canal or tunnel) from which the penstock takes off. It stores water to meet sudden load demand, provides the transition from open-channel flow to pressure flow, and provides a place for the trash rack, the spillway and sediment flushing.

Design procedure

1. Decide the discharge and retention time: $Q$ = turbine discharge; the retention time $t$ is usually 2-3 minutes at full load.
2. Volume of storage: $V=Q\,t$
3. Cross-section: limit the velocity in the forebay to $v\le0.2-0.3$ m/s, so that sediment settles and the flow is calm: $A=Q/v$
4. Water depth from the submergence of the penstock intake:
   • velocity in the penstock, $V_p=\dfrac{Q}{n\,\frac{\pi}{4}D^2}$ ($n$ = number of penstocks)
   • Gordon's formula $S=C\,V_p\sqrt D$ ($C=0.5434$ for a symmetrical approach and 0.7245 for an asymmetrical approach)
   • depth $H=S+D+$ bottom clearance (0.3-0.5 m)
5. Width and length: $B=\dfrac{A}{H}$ and $L=\dfrac{V}{A}$ (check that $L/B$ is large enough, around 2-4, with a gradual expansion from the headrace).
6. Spillway: to pass the full design discharge when the turbines trip, $Q=C\,L_s\,h^{3/2}$ with $C\approx1.7$ for a broad crest and $h=0.3-0.5$ m.
7. Free board (0.5 m), a bottom slope towards a flushing gate, a trash rack at the intake and an air vent behind the penstock gate.
8. Check the entrance loss, and set the top of the forebay wall at full supply level + surge + free board.

Sketch

PLAN
 headrace ====> \  forebay  /|==> penstock
        transition| rack     |
 ====>           /           |==> penstock
              spillway  |  flush gate
                        v to river

SECTION
 FSL ~~~~~~~~~~~~~~~~~~~~~~~~~~
      |      S      |rack|gate
      |             |####|  ___ penstock crown
 bed  |_____________|####|_/ D
        0.5 m clearance