# Pipe Sizing for Air

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

### Air Pressure Loss through Piping formula

$$\large{ p_l = \frac { \mu \; \cdot \; l \; \cdot \; v_a{^2} \; \cdot \; \rho } {2d } }$$

Where:

$$\large{ p_l }$$ = air pressure loss

$$\large{ \rho }$$  (Greek symbol rho) = density of the air

$$\large{ \mu }$$  (Greek symbol mu) = friction coefficient

$$\large{ d }$$ = pipe inside diameter

$$\large{ l }$$ = pipe length

$$\large{ v_a }$$ = velocity of the air

### Air Pipe Inside Diameter formula

$$\large{ d = \sqrt { \frac { 4 } { \pi } \; \cdot \; \frac { Q_a } {60v_a} } }$$

Where:

$$\large{ d }$$ = pipe inside diameter

$$\large{ \pi }$$ = Pi

$$\large{ Q_a }$$ = flow rate of the air

$$\large{ v_a }$$ = velocity of the air

### Air Velocity through Piping formula

$$\large{ v_a = \frac { Q_a } { 60 \pi { \left( \frac {d}{2} \right) ^2 } } }$$

Where:

$$\large{ v_a }$$ =  velocity of the air

$$\large{ Q_a }$$ = flow rate of the air

$$\large{ \pi }$$ = Pi

$$\large{ d }$$ = pipe inside diameter

### Air Flow Rate through Piping formula

$$\large{ Q_a = 60 \pi \cdot v_a { \left( \frac {d}{2} \right) ^2 } }$$

Where:

$$\large{ Q_a }$$ = flow rate of the air

$$\large{ \pi }$$ = Pi

$$\large{ d }$$ = pipe inside diameter

$$\large{ v_a }$$ = velocity of the air