# Pipe Equations

## Calculate cross-sectional areas, weight of empty pipes, weight of pipes filled with water, inside and outside surface areas

### Cross Sectional inside Pipe Area

Cross-sectional inside area of a pipe can be calculated as

A_{i}= π (d_{i}/ 2)^{2 }

=(1)dπ_{i}^{2}/ 4

where

A_{i}= cross-sectional inside area of pipe (m^{2}, in^{2})

d_{i}= inside diameter (m, in)

### Cross Sectional Pipe Wall Area

The cross-sectional wall area - or area of piping material - can be calculated as

A_{m}=π (d- π (d_{o}/ 2)^{2 }_{i}/ 2)^{2 }

=(πd- d_{o}^{2}_{i}^{2}) / 4 (2)

where

A_{m}= cross-sectional wall area of pipe (m^{2}, in^{2})

d_{o}= outside diameter (m, in)

### Weight of Empty Pipes

Weight of empty pipes per unit length can be calculated as

w_{p}=ρ_{m}A_{m}

=(ρ_{m}π (d- π (d_{o}/ 2)^{2 }_{i}/ 2)^{2})

=ρ_{m}(3)π (d- d_{o}^{2 }_{i}^{2}) / 4

where

w_{p}= weight of empty pipe per unit length (kg/m, lb/in)

= density of pipe material (kg/mρ_{s}^{3}, lb/in^{3})

### Weight of Liquid in Pipes

Weight of liquid in pipes per unit length can be calculated as

w_{l}=ρ_{l}A

=ρ_{l}π (d_{i}/ 2)^{2}

=ρ_{l}(4)πd_{i}^{2}/ 4

where

w_{l}= weight of liquid in pipe per unit length of pipe (kg, lb)

= density of liquid (kg/mρ_{l}^{3}, lb/in^{3})

### Weight of Pipe filled with Liquid

Weight of pipe filled with liquid per unit length can be calculated as

*w = w _{l} + w_{p} (5)*

*where *

*w = weight of pipe and liquid per unit length of pipe (kg, lb) *

### Outside Surface Area of Pipes

Outside surface area of steel pipes per unit length can be calculated as

A_{o}= 2 π (d_{o}/ 2)

=π d(6)_{o}

where

A_{o}= outside area of pipe - per unit length of pipe (m^{2}, in^{2})

### Inside Surface Area of Pipes

Inside surface area of steel pipes per unit length can be calculated as

A_{i}=2 π (d_{i}/ 2)

=π d(7)_{i}

where

A_{i}= inside area of pipe -per unit length of pipe(m^{2}, in^{2})