Pipe Equations
Calculate crosssectional areas, weight of empty pipes, weight of pipes filled with water, inside and outside surface areas.
Cross Sectional inside Pipe Area
Crosssectional 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} = crosssectional inside area of pipe (m^{2}, in^{2})
d_{i} = inside diameter (m, in)
Cross Sectional Pipe Wall Area
The crosssectional 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} = crosssectional 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_{o} / 2)^{2 }  π (d_{i} / 2)^{2})
= ρ_{m} π (d_{o}^{2 }  d_{i}^{2}) / 4 (3)
where
w_{p} = weight of empty pipe per unit length (kg/m, lb/in)
ρ_{s} = density of pipe material (kg/m^{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} π d_{i}^{2} / 4 (4)
where
w_{l} = weight of liquid in pipe per unit length of pipe (kg, lb)
ρ_{l} = density of liquid (kg/m^{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_{o} (6)
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_{i} (7)
where
A_{i} = inside area of pipe  per unit length of pipe (m^{2}, in^{2})
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