The discharge through a Francis turbine depends on
- Aa factor that allows for the thickness of the vanes
- Bthe velocity of flow
- Cboth (A) and (B)Correct
- Dnone of the above
Solution
Concept
Francis Turbine Discharge Formula and Flow Area Efficiency
Formula
Yes, the formula for discharge (Q) through a Francis turbine accounting for vane thickness is Q = k × π × D1 × B1 × Vf1 or Q = (π × D1 - n × t) × B1 × Vf1, where D1 is the runner diameter at inlet, B1 is the runner width at inlet, Vf1 is the velocity of flow at inlet, n is the number of vanes, t is the vane thickness, and k is the vane thickness factor.
Step-by-step solution
1. Identify the net flow area at the inlet, accounting for vane thickness: Area = (π \* D1 - n \* t) \* B1. 2. Multiply the net flow area by the flow velocity: Discharge (Q) = Area \* Vf1. 3. Observe that Q depends on both the velocity of flow (Vf1) and the vane thickness factor.
Explanation
The discharge through a Francis turbine depends on both the velocity of flow and a factor accounting for the thickness of the vanes.1. Velocity of Flow: The speed at which water moves through the turbine directly determines how much water passes through in a given time. 2. Thickness of Vanes: The physical blades (vanes) inside the turbine occupy space, reducing the actual area available for water to flow through. Therefore, a blade thickness factor must be included to accurately calculate the discharge area.Since both the flow velocity and the net flow area (adjusted for vane thickness) dictate the total volume of water passing through, option C ("both (A) and (B)") is correct.
Shortcut
Remember "Discharge = Area x Velocity" (Q = A x V): - Velocity (V) comes from the velocity of flow. - Area (A) depends on space available, which requires subtracting the vanes' thickness Therefore, discharge depends on both velocity of flow and vane thickness.
Correct answer: C) both (A) and (B)