Forebay design considerations; design for 12 m³/s

Design considerations of a forebay

• Storage: enough volume for the retention time (2-3 min) to meet a sudden load increase until the headrace flow adjusts.
• Low velocity (0.2-0.3 m/s), so that the remaining sediment settles and the flow at the intake is calm.
• Adequate submergence of the penstock intake below the minimum water level to avoid vortices and air entry (Gordon's rule), with a trash rack and a smooth bell-mouth.
• Spillway able to pass the design flow on load rejection, with a safe discharge channel.
• Flushing/desilting arrangement at the bottom (flushing gate and bed slope) and a bottom clearance of about 0.5 m.
• Stable foundation, water-tightness (lining), 0.5 m free board and access for maintenance; located on firm ground close to the powerhouse and protected from slides.

Design for the given data

Given: $Q=12.0$ m³/s; 2 penstocks of diameter 2.0 m; retention (detention) time 3 min; limiting velocity in the forebay 0.20 m/s.

Step 1: Volume of the forebay

The forebay stores the water for the retention time:

$$V=Q\,t=12.0\times(3\times60)=2160\ \text{m}^3$$

Step 2: Cross-sectional area from the velocity limit

$$A=\frac{Q}{v}=\frac{12.0}{0.20}=60.0\ \text{m}^2$$

Step 3: Depth of water (submergence of the penstock intake)

Velocity in each penstock: $V_p=\dfrac{Q}{2\times\frac{\pi}{4}D^2}=1.910$ m/s. Minimum submergence to avoid vortices (Gordon, with $C=0.7245$ for an asymmetrical approach, which is on the safe side):

$$S=0.7245\,V_p\sqrt{D}=0.7245\times1.910\times\sqrt{2.0}=1.96\ \text{m}$$

Water depth = $S+D+$ bottom clearance of 0.5 m $=1.96+2.0+0.5=4.46$ m, adopt $H=4.5$ m.

Step 4: Width and length

$$B=\frac{A}{H}=\frac{60.0}{4.5}=13.33\ \text{m},\qquad L=\frac{V}{A}=\frac{2160}{60.0}=36.0\ \text{m}$$

Adopt $B=13.5$ m and $L=36$ m (the volume is then $B\,L\,H=2187$ m³ $\ge V$).

PLAN
 headrace        forebay                 penstocks
 tunnel/canal  +------------------+
 ====> \       |                  |==> penstock 1
        \ trans| trash rack       |
 ====> /       |                  |==> penstock 2
              +--+-spillway-+-flush+
                   |          |
                   v          v  to river (spillway/flushing)

SECTION
 canal bed ____ WL ~~~~~~~~~~~~~~~~~~~~~~
                  |        S (submergence)
                  |   rack  ____ crown
                  |   ####  \   penstock
 flushing  ______ |___####____\_D__
 bottom clearance 0.5 m

Answer: forebay about 36 m long x 13.5 m wide x 4.5 m deep (water), with a volume of 2160 m³.