...
| Steady-State flow | Isothermal |
| LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle \frac%7B\partial p%7D%7B\partial t%7D = 0 \rightarrow p(t,l) = p(l) |
|---|
|
| | LaTeX Math Inline |
|---|
| body | T(t, l)=T_0 = \rm const |
|---|
|
|
| Homogenous flow | |
| LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle \frac%7B\partial p%7D%7B\partial \tau_x%7D =\frac%7B\partial p%7D%7B\partial \tau_y%7D =0 \rightarrow p(t, \tau_x,\tau_y,l) = p(l) |
|---|
|
| |
| Incompressible fluid |
| LaTeX Math Inline |
|---|
| body | \rho(T, p)=\rho_0 = \rm const |
|---|
|
→ | LaTeX Math Inline |
|---|
| body | \mu(T, \rho) =\mu_0 = \rm const |
|---|
|
|
...
| Pressure profile | Pressure gradient profile |
|---|
| LaTeX Math Block |
|---|
| anchor | PPconst |
|---|
| alignment | left |
|---|
| p(l) = p_0 + \rho_0 \, g \, \Delta z(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 \, l = p_0 + \rho_0 \, g \, \Delta z(l) - \frac{8}{\pi^2} \frac{f_0 \, l}{d^5} \rho_0 \, q_0^2 |
| | LaTeX Math Block |
|---|
| \frac{dp}{dl} = \rho_0 \, g \cos \theta(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 |
|
| Mass Flux | Mass Flowrate |
| LaTeX Math Block |
|---|
| anchor | MassFlux |
|---|
| alignment | left |
|---|
| j_m = \rho_0 \cdot \sqrt{\frac{2 \, d}{f_0 \, l }} \cdot \sqrt{g \, \Delta z(l) + (p_0 - p)/ \rho_0}
|
| | LaTeX Math Block |
|---|
| anchor | MassFlowrate |
|---|
| alignment | left |
|---|
| \dot m = j_m \cdot A = \rho_0 \cdot A \cdot \sqrt{\frac{2 \, d}{f_0 \, l }} \cdot \sqrt{g \, \Delta z(l) + (p_0 - p)/ \rho_s}
|
|
Volumetric Flowrate | Intake Fluid velocity |
| LaTeX Math Block |
|---|
| anchor | PPconst |
|---|
| alignment | left |
|---|
| q_0 = \dot m / \rho_0 = A \cdot \sqrt{\frac{2 \, d }{ f_0 \, l }} \cdot \sqrt{ g \, \Delta z(l) + (p_0 - p)/ \rho_s0 }
|
| | LaTeX Math Block |
|---|
| anchor | PPconst |
|---|
| alignment | left |
|---|
| u_0 = j_m/ \rho_0 =q_0 / A = \sqrt{\frac{2 \, d }{ f_0 \, l }} \cdot \sqrt{ g \, \Delta z(l) + (p_0 - p)/ \rho_s }
|
|
...
...
