ANS:A - C_v . 2gH

The actual velocity at the vena contracta (the point where the cross-sectional area of flow is the smallest downstream of an orifice) for flow through an orifice from a reservoir is given by: Cd2gHC_d \sqrt{2gH}Cd​2gH​ where:

• CdC_dCd​ is the discharge coefficient of the orifice,
• ggg is the acceleration due to gravity,
• HHH is the height of fluid above the center of the orifice.

Explanation:

1. Discharge Coefficient (CdC_dCd​):
   • The discharge coefficient CdC_dCd​ accounts for losses due to friction, contraction, and other factors affecting the flow through the orifice. It is dimensionless and typically less than 1.
   • CdC_dCd​ is determined experimentally and varies with the shape and size of the orifice.
2. Velocity Calculation:
   • The velocity at the vena contracta can be derived using Bernoulli's equation, taking into account the pressure difference between the reservoir and the orifice exit.
   • For an orifice, the velocity can be expressed as 2gH\sqrt{2gH}2gH​, where HHH is the height of the fluid column above the orifice.
3. Relationship:
   • The actual velocity VVV at the vena contracta is related to the discharge coefficient CdC_dCd​ and the square root of the head HHH: V=Cd2gHV = C_d \sqrt{2gH}V=Cd​2gH​
   • This formula accounts for the effective area of flow at the vena contracta, which is typically smaller than the area of the orifice due to contraction effects.

Conclusion: