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. The diameter ratio \(\beta\) is the ratio of the orifice diameter to the pipe diameter.

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

\begin{equation}\label{eq:flow-calculations-diameter-ratio} \beta = \frac{d_{orifice}}{d_{pipe}}\end{equation}

Symbols

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