# Piping Geometry Factor

on . Posted in Dimensionless Numbers

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

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

### 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)

Symbol 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, upstream and downstream $$\large{ in }$$ $$\large{ mm }$$

### 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) 