...
Let's start with Pressure Profile in Homogeneous Steady-State Pipe Flow @model:
| LaTeX Math Block |
|---|
| \left[\rho(p) - j_m^2 \cdot c(p) \right] \frac{dp}{dl} = \rho^2(p) \, g \, \cos \theta(l) - \frac{ j_m^2 }{2 d} \cdot f(p) |
|
| LaTeX Math Block |
|---|
| p(l=0) = p_0 |
|
| LaTeX Math Block |
|---|
| u(l) = \frac{j_m}{\rho(l)} |
|
| LaTeX Math Block |
|---|
| q(l) =A \cdot u(l) |
|
and assume constant pipe inclination:
| LaTeX Math Block |
|---|
|
\theta(l) = \theta = \rm const |
Let's define constant number:
| LaTeX Math Block |
|---|
|
G = g \cdot \cos \theta = \rm const |
| LaTeX Math Block |
|---|
| anchor | PressureProfile |
|---|
| alignment | left |
|---|
|
L = \int_{\rho_0}^{\rho} \frac{1/c- j_m^2 / \rho}{G \, \rho^2 - F} \, d \rho
=\int_{\rho_0}^{\rho} \frac{\rho \, dp}{G \, \rho^2 - F} -\frac{j_m^2}{2} \, \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G} |
...
