If the discharge coefficient C_d for an orifice is less than 1, what does this indicate about the discharge?

If the discharge coefficient C_d for an orifice is less than 1, what does this indicate about the discharge?

• A. The actual discharge is higher than ideal.
• B. The orifice is functioning as a perfect nozzle.
• C. The actual discharge is lower than ideal due to non-ideal losses such as vena contracta and turbulence.
• D. The flow is frictionless.

Answer: (C)

When the discharge coefficient is less than one, the actual flow rate through the orifice is smaller than the ideal flow rate for the same head. In real flow, energy is lost as the jet exits the orifice: the jet contracts at the vena contracta, and turbulence and viscous effects dissipate energy. These non-ideal losses reduce the discharge from its ideal value, so Q_actual = C_d × Q_ideal with C_d < 1. This is why the correct interpretation is that the actual discharge is lower than ideal due to losses such as vena contracta and turbulence. If flow were frictionless or the device behaved like a perfect nozzle, the discharge coefficient would be about 1, and the actual discharge would match the ideal.

When the discharge coefficient is less than one, the actual flow rate through the orifice is smaller than the ideal flow rate for the same head. In real flow, energy is lost as the jet exits the orifice: the jet contracts at the vena contracta, and turbulence and viscous effects dissipate energy. These non-ideal losses reduce the discharge from its ideal value, so Q_actual = C_d × Q_ideal with C_d < 1.

This is why the correct interpretation is that the actual discharge is lower than ideal due to losses such as vena contracta and turbulence. If flow were frictionless or the device behaved like a perfect nozzle, the discharge coefficient would be about 1, and the actual discharge would match the ideal.