When the orifice diameter is smaller than the pipe diameter, the discharge coefficient must be adjusted to account for the velocity of approach and contraction effects. If the diameters are equal, no adjustment is needed.

\begin{equation}\label{eq:flow-calculations-adjusted-discharge-coeff} C_{d,adj} = \begin{cases} \frac{C_d}{\sqrt{1 - \left(\frac{d_{orifice}}{d_{pipe}}\right)^4}} & \text{if } d_{orifice} < d_{pipe} \\ C_d & \text{otherwise} \end{cases}\end{equation}

Symbols

\(C_{d,adj}\)	Adjusted discharge coefficient \([\unit{ \unitless}]\)
\(C_d\)	Discharge coefficient \([\unit{ \unitless}]\)
\(d_{orifice}\)	Orifice diameter \([\unit{ \inch}]\)
\(d_{pipe}\)	Inside pipe diameter \([\unit{ \inch}]\)