(1) | \left( \frac{dp}{dl} \right)_f = - \frac{ j_m^2}{2 d} \cdot \frac{f}{\rho} |
The friction losses depend on density and friction factor distribution along the pipe.
The accurate calculations require solving of a self-consistent equation of Pressure Profile in Homogeneous Quasi-Isothermal Steady-State Pipe Flow @model.
There are few popular practical approximations based on assumption of constant friction factor and linear density-pressure equation of state.
Approximations
|
| f(l)= f_0 = \rm const \rho(l)=\rho_0= \rm const | ||||
|
| f(l)= f_0 = \rm const \rho(l)=\rho^* \cdot (1 + c^* \, p) |
See also
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Pressure Profile in Homogeneous Quasi-Isothermal Steady-State Pipe Flow @model
[ Darcy friction factor ] [ Darcy friction factor @model ] [ Reynolds number in Pipe Flow ]