# Lechapt and Calmon

This module allows to calculate the pressure losses in a circular pipe from the Lechapt and Calmon abacuses.

It allows the calculation of the value of one of the following quantities:

• Flow rate (m3/s)
• Pipe diameter (m)
• Total head loss (m)
• Pipe length (m)
• Singular pressure loss coefficient (m)

The total head loss is the sum of the linear head losses $$J_L$$ obtained from the Lechapt and Calmon abacuses and singular $$J_S$$ depending on the above coefficient.

## Lechapt and Calmon abacuses

Lechapt and Calmon formula is based on adjustements of Cyril Frank Colebrook formula:

$J_L=\frac{l_T}{1000}L.Q^M.D^{-N}$

With:

• $$J_L$$: headloss in mm/m or m/km;
• $$l_T$$: pipe length in m;
• $$Q$$: flow in L/s;
• $$D$$: pipe diameter in m;
• $$L$$, $$M$$ and $$N$$ coefficients depending on roughness {ϵ}.

The error made with respect to the Colebrook formula is less than 3% for speeds between 0.4 and 2 m/s.

The correlation table of the coefficients is as follows:

Material ϵ (mm) $$L$$ $$M$$ $$N$$
Uncoated cast iron or steel - Coarse concrete (corrosive water) 2 1.863 2 5.33
Uncoated cast iron or steel - Coarse concrete (low corrosive water) 1 1.601 1.975 5.25
Cast iron or steel with cement coating 0.5 1.40 1.96 5.19
Cast iron or steel bitumen coating - centrifuged concrete 0.25 1.16 1.93 5.11
Rolled steel - smooth concrete 0.1 1.10 1.89 5.01
Cast iron or steel centrifugal coating 0.05 1.049 1.86 4.93
PVC - polyethylene 0.025 1.01 1.84 4.88
Hydraulically smooth pipe - 0.05 ≤ D ≤ 0.2 0.00 0.916 1.78 4.78
Hydraulically smooth pipe - 0.25 ≤ D ≤ 1 0.00 0.971 1.81 4.81

Table: Materials and coefficients used in the Lechapt and Calmon formula

## Singular head loss

$J_S = K_S \frac{V^2}{2g}$

With:

• $$K_S$$ : singular head loss coefficient
• $$V$$ : water speed in the pipe ($$V = 4 Q / \pi / D^2$$)

## Darcy's head loss coefficient

 f_D = \frac{2g J D}{l_T V^2}