The correct answer is: A. slightly less.
The coefficient of discharge is a dimensionless number that is used to relate the theoretical discharge of an orifice to the actual discharge. The coefficient of discharge is always less than 1, and it is affected by a number of factors, including the orifice geometry, the upstream pressure, and the downstream pressure.
For a totally submerged orifice, the coefficient of discharge is slightly less than for an orifice discharging free. This is because the pressure at the upstream face of the orifice is equal to the pressure in the surrounding fluid, which reduces the driving force for the flow.
The following is a brief explanation of each option:
- Option A: Slightly less. The coefficient of discharge for a totally submerged orifice is slightly less than for an orifice discharging free. This is because the pressure at the upstream face of the orifice is equal to the pressure in the surrounding fluid, which reduces the driving force for the flow.
- Option B: Slightly more. The coefficient of discharge for a totally submerged orifice is slightly more than for an orifice discharging free. This is not correct. The coefficient of discharge for a totally submerged orifice is slightly less than for an orifice discharging free.
- Option C: Nearly half. The coefficient of discharge for a totally submerged orifice is nearly half of that for an orifice discharging free. This is not correct. The coefficient of discharge for a totally submerged orifice is slightly less than for an orifice discharging free.
- Option D: Equal. The coefficient of discharge for a totally submerged orifice is equal to that for an orifice discharging free. This is not correct. The coefficient of discharge for a totally submerged orifice is slightly less than for an orifice discharging free.