...
See Derivation of Pressure Profile in Stationary Isothermal Homogenous Pipe Flow @model.
Alternative forms
| LaTeX Math Block |
|---|
|
-\frac{1}{c} \frac{d}{dl} \left( \frac{1}{\rho} \right) + \frac{\rho_s^2 q_s^2}{2A^2} \frac{d}{dl} \left( \frac{1}{\rho^2} \right) + \frac{\rho_s^2 q_s^2}{2A^2} \frac{f}{d} \left( \frac{1}{\rho^2} \right) - g \frac{dz}{dl} = 0 |
See derivation at
| LaTeX Math Block Reference |
|---|
| anchor | drho |
|---|
| page | Derivation of Pressure Profile in Stationary Quasi-Isothermal Homogenous Pipe Flow @model |
|---|
|
.It does not give much benefit in computations comparing to
| LaTeX Math Block Reference |
|---|
|
but it makes a starting point for derivation of some popular proxy models (like Slightly Compressible Fluid and Ideal Gas).
Approximations
...
Incompressible pipe flow
with constant viscosity ...
