# Using Fritzsche equation to calculate Air pressure drop in piping systems

Fritzsche equation used below to calculate the pressure drop in Air piping system. Various equations have been used to calculate the pressure drop in pipes. The purpose of this short article is show this equation to users. while some may not find it the most effective method to calculate pressure drops however this equation is used for different compressed gases in piping systems. The equations below are for Air piping system.

## Fritzsche equation

The equation can be expressed as below:

$∆P\ =\ \frac{\left(9.8265\ x\ 10^{-4}\right)\ T\ L}{P\ d^5}\left(\frac{Ps\ Qs}{Ts}\right)^{1.857}$

Where;
∆P = pressure drop, psi
L = pipe length, ft
d = pipe inside diameter, in
T = air flow temperature, 'R
P = average air pressure, psia
Qs = volume flow rate at standard conditions, SCFM
Ps = pressure at standard conditions, psia
Ts = temperature at standard conditions, 'R


If the standard conditions of pressure and temperature are at 14.7 psia and 60oF the equation is simplified to

$∆P\ =\ \frac{L\ Qs^{1.857}}{1480\ P\ d^5}$

Where;
∆P = pressure drop, psi
L = pipe length, ft
P = average air pressure, psia
Qs = volume flow rate at standard conditions, SCFM
d = pipe inside diameter, in

## Fritzsche equation expresses in terms of flow

Expressing the Fritzsche equation in terms of flow rate

$Qs\ =\ 29.167\ \frac{Ts}{Ps}\left[\frac{\left(P1^{2\ }-\ P2^2\right)\ d^5}{T\ L}\right]^{^{0.538}}$

Where;
Qs = volume flow rate at standard conditions, SCFM
Ps = pressure at standard conditions, psia
Ts = temperature as standard conditions, 'R
P1 = upstream pressure, psia
P2 = downstream pressure, psia
L = pipe length, ft
d = pipe inside diameter, in
T = airflow temperature, 'R


And if the standard conditions of pressure and temperature are at 14.7 psia and 60oF the equation is simplified to

$Qs\ =\ \frac{1}{35}\left[\frac{\left(P1^2-P2^2\right)\ d^5}{L}\right]^{0.538}$

Where;
Qs = volume flow rate at standard conditions, SCFM
P1 = upstream pressure, psia
P2 = downstream pressure, psia
L = pipe length, ft
d = pipe inside diameter, in

## Fritzche friction factor

Fritzche equation friction factor can be calculated from the following equation;

$f\ =\ 0.02993\ \left(\frac{Ts}{Ps\ Qs}\right)^{\frac{1}{7}}$

Where;
f = friction factor
Ts = temperature at standard conditions, 'R
Ps = pressure at standard conditions, SCFM
Qs = volume flow rate at standard conditions, SCFM

## Refrences

E. Shashi Menon, Piping Calculations Manual, McGraw-Hill, 2005