Piping Equations

Cross Sectional inside Pipe Area

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

A_i = π (d_i / 2)²

   = π d_i ²/ 4                                 (1)

where

A_i = cross-sectional inside area of pipe (m², in²)

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_o / 2)² - π (d_i / 2)²

   = π (d_o ² - d_i ²) / 4                               (2)

where

A_m = cross-sectional wall area of pipe (m², in²)

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_o / 2)² - π (d_i / 2)²) 

    = ρ_m π (d_o² - d_i²) / 4                              (3)

where

w_p = weight of empty pipe per unit length (kg/m, lb/in)

ρ_s = density of pipe material (kg/m³, lb/in³)

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 π d_i² / 4                                   (4)

where

w_l = weight of liquid in pipe per unit length of pipe (kg, lb)

ρ_l = density of liquid (kg/m³, lb/in³)

• water content in pipes

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_o                            (6)

where

A_o = outside area of pipe - per unit length of pipe (m², in²)

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_i                             (7)

where

A_i = inside area of pipe - per unit length of pipe (m², in²)