Piping Geometry Factor

Piping geometry factor, abbreviated as \(F_p\), a dimensionless number, is the pressure and velocity changes caused by fittings such as bends, expanders, reducers, tees, and Y's if directly conected to the valve.  

 

Piping Geometry Factor Formula

\(\large{ F_p = \frac{1}{  \sqrt{1\;+\;\frac{\Sigma K}{0.00214} \; \left( \frac{C_v}{D_v^2}   \right)^2   }   }   }\)

Where:

Units	English	Metric
\(\large{ F_p }\) = piping geometry factor	\(\large{ dimensionless }\)
\(\large{ D_v  }\) = nominal valve size	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ C_v }\) = flow coefficient	\(\large{ dimensionless }\)
\(\large{ \Sigma K }\) = algebraic sum	-	-

Solve for:

\(\large{ \Sigma K = K_1 + K_2 + K_{B1} + K_{B2}   }\)
\(\large{ \Sigma K }\)	(the algebraic sum of the velocity head loss coefficient for all the fittings that are attached to the valve)

Where:

Units	English	Metric
\(\large{ K_1 }\) = resistance coefficient of upstream fittings	\(\large{ dimensionless }\)
\(\large{ K_2 }\) = resistance coefficient of downstream fittings	\(\large{ dimensionless }\)
\(\large{ K_{B1} }\) = inlet Bernoulli coefficient	\(\large{ dimensionless }\)
\(\large{ K_{B2} }\) = outlet Bernoulli coefficient	\(\large{ dimensionless }\)
\(\large{ D_v }\) = nominal valve size	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ d }\) = pipe inside diameter	\(\large{ in }\)	\(\large{ mm }\)

Solve for:

\(\large{ K_1  = 0.5 ;\ \left( 1 - \frac{D_v^2}{d^2} \right)^2   }\)	(inlet expander / reducer)
\(\large{ K_1  = 1.0 \; \left( 1 - \frac{D_v^2}{d^2} \right)^2   }\)	(outlet expander / reducer)
\(\large{ K_1 + K_1  = 1.5 \; \left( 1 - \frac{D_v^2}{d^2} \right)^2   }\)	(for a valve installed between identical expander / reducer)
\(\large{ K_{B1} }\) or \(\large{ K_{B2}  = 1 - \left( \frac{D_v}{d} \right)^4   }\)
\(\large{ K_{B1} }\) or \(\large{ K_{B2} }\)	(are only used when the diameter of the piping approaching the valve is different from the diameter of the piping leaving the valve)