--- title: "Forebay design considerations; design for 12 m³/s" subject: "Hydropower Engineering" chapter: 6 key: "semester_7/hydropower_engineering:forebay-design-considerations-12cumec" source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/forebay-design-considerations-12cumec site: BCT Engineering --- # Forebay design considerations; design for 12 m³/s Hydropower Engineering · Chapter 6: Water Conveyance Structures - Asked in: 2070 Chaitra, 2+4 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/forebay-design-considerations-12cumec - Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-6 ## Question What are the design considerations of a forebay? Design a forebay with turbine discharge 12 m³/sec, water is conveyed from the forebay to the powerhouse by two penstocks of 2 m diameter each. Take retention time 3 minutes and limiting velocity 0.2 m/sec. ## Short answer Required volume = 12 × 180 = 2160 m³; limiting velocity 0.2 m/s gives area 60 m². Submergence 1.96 m, water depth 4.5 m. Forebay 36 m long × 13.5 m wide × 4.5 m deep. ## Answer #### 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 $\ge V$). ```text 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 ``` | Item | Value | |---|---| | Storage volume | 2160 m³ | | Water depth | 4.5 m (+0.5 m free board) | | Width | 13.5 m | | Length | 36 m | | Submergence of penstock crown | 1.96 m | **Answer**: forebay about 36 m long x 13.5 m wide x 4.5 m deep (water), with a volume of 2160 m³. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the velocity in a forebay kept low (about 0.2-0.3 m/s)? A. To reduce the volume of the forebay B. To increase the discharge to the turbine C. To let remaining sediment settle and keep the flow calm at the intake D. To increase the head at the penstock Answer: C. Low velocity lets sediment settle and gives calm flow at the penstock intake. (Key point: Low velocity) 2. What is the purpose of adequate submergence of the penstock intake below minimum water level? A. To flush sediment B. To avoid vortices and air entry C. To store more water D. To raise the gross head Answer: B. Sufficient submergence (Gordon's rule) prevents vortex formation and air entering the penstock. (Key point: Submergence) 3. Why is a forebay spillway designed for the full design flow? A. To measure discharge B. To pass the water when the turbines reject load, with a safe discharge channel C. To lower the sediment level D. To increase retention time Answer: B. On load rejection the inflow continues, so the whole discharge must spill safely. (Key point: Spillway) 4. For Q = 12 m^3/s, 3 min retention and 0.2 m/s limit, what are the storage volume and flow area? A. V = 720 m^3, A = 60 m^2 B. V = 2160 m^3, A = 2.4 m^2 C. V = 2160 m^3, A = 60 m^2 D. V = 36 m^3, A = 2160 m^2 Answer: C. V = 12 x 180 = 2160 m^3 and A = 12/0.2 = 60 m^2. 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