Inputs & Outputs

Inputs		Outputs
$\begin{array}{l}T_s\end{array}$	Intake temperature	$\begin{array}{l}T(l)\end{array}$	Temperature distribution along the pipe
$\begin{array}{l}p_s\end{array}$	Intake pressure
$\begin{array}{l}q_s\end{array}$	Intake flowrate
$\begin{array}{l}z(l)\end{array}$	Pipeline trajectory TVDss
$\begin{array}{l}\theta (l)\end{array}$	Pipeline trajectory inclination, $\begin{array}{l}\displaystyle \cos \theta (l) = \frac{dz}{dl}\end{array}$
$\begin{array}{l}\rho(T, p)\end{array}$	Fluid density
$\begin{array}{l}\mu(T, p)\end{array}$	Fluid viscosity
$\begin{array}{l}d\end{array}$	Flow pipe diameter (tubing or casing depending on where flow occurs)
$\begin{array}{l}\epsilon\end{array}$	Inner pipe wall roughness

Assumptions

Stationary fluid flow		Isothermal or Quasi-isothermal conditions	Constant cross-section pipe area $\begin{array}{l}A\end{array}$ along hole
Incompressible fluid $\begin{array}{l}\rho(T, p)=\rho_s = \rm const\end{array}$	Isoviscous $\begin{array}{l}\mu(T, p) = \mu_s = \rm const\end{array}$

(1)	$\begin{array}{l}\displaystyle T(l) = Ts + ...\end{array}$

where