This articles demonstrates how to determine pressure losses through drill string.
To determine pressure drop while the drilling mud is passing through a circular pipe (drill pipe and drill collar), you can calculate pressure loss with the following equation:
Turbulent viscosity = 3 cp
Friction factor = 0.378(Q/D)-0.14
The first equation has a coefficient (C) to take into account the friction and the geometry of the bore ID.
P = pressure loss, psi
L = length of pipe, ft
W = mud density, ppg
Vf = viscosity correction factor
PV = plastic viscosity, centipoises
Q = flow rate, gpm
Di = inside diameter of pipe, inch
C = general coefficient for internal diameter of pipe