The discharge through an orifice can be calculated using the formula \(\rm Q=C_dA\sqrt{2gh}\), where Q is the discharge, C_d is the discharge coefficient, A is the cross-sectional area of the orifice, g is the acceleration due to gravity, h is the head of the liquid above the orifice. If the actual measured discharge is lower than the theoretical discharge, which of the following could be true?

Concept:

The actual discharge through an orifice is generally lower than the theoretical discharge due to energy losses such as:

• Friction losses within the orifice.
• Flow contraction (vena contracta effect) reducing the effective flow area.
• Viscous effects in real fluids.

Theoretical discharge is given by Torricelli’s theorem:

\( Q_{\text{theoretical}} = A \sqrt{2gh} \)

The actual discharge is calculated using the discharge coefficient \( C_d \):

\( Q_{\text{actual}} = C_d A \sqrt{2gh} \)

Since real flow experiences losses, the coefficient of discharge \( C_d \) is always less than 1.