# 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

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

Where:

\(\large{ F_p }\) = piping geometry factor

\(\large{ d }\) = nominal valve size

\(\large{ C_v }\) = flow coefficient

\(\large{ \Sigma K }\) = algebraic sum

Solve for:

\(\large{ \Sigma K = K_1 + K_2 + K_{B1} + K_{B2} }\)

\(\large{ \Sigma K }\) is the algebraic sum of the velocity head loss coefficient for all the fittings that are attached to the valve.

Where:

\(\large{ K_1 }\) = resistance coefficient of upstream fittings

\(\large{ K_2 }\) = resistance coefficient of downstream fittings

\(\large{ K_{B1} }\) = inlet Bernoulli coefficient

\(\large{ K_{B2} }\) = outlet Bernoulli coefficient

\(\large{ d }\) = nominal valve size

\(\large{ D }\) = pipe inside diameter (ID)

Solve for:

\(\large{ K_1 = 0.5 ;\ \left( 1 - \frac{d^2}{D^2} \right)^2 }\) (inlet expander/reducer)

\(\large{ K_1 = 1.0 \; \left( 1 - \frac{d^2}{D^2} \right)^2 }\) (outlet expander/reducer)

\(\large{ K_1 + K_1 = 1.5 \; \left( 1 - \frac{d^2}{D^2} \right)^2 }\) (for a valve installed between identical expander/reducer)

\(\large{ K_{B1} }\) or \(\large{ K_{B2} = 1 - \left( \frac{d}{D} \right)^4 }\)

\(\large{ K_{B1} }\) 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.