...
Low compressible fluids: LaTeX Math Inline |
---|
body | --uriencoded--c%5e* p \ll 1, \, \, c%5e* p_0 \ll 1 |
---|
|
| High compressible fluids: LaTeX Math Inline |
---|
body | --uriencoded--c%5e* p \gg 1, \, \, c%5e* p_0 \gg 1 |
---|
|
|
LaTeX Math Inline |
---|
body | --uriencoded--\displaystyle \rho_0/\rho = c%5e* \cdot (p_0-p) |
---|
|
| LaTeX Math Inline |
---|
body | \displaystyle \rho_0/\rho = p_0/p |
---|
|
|
Approximations
...
|
LaTeX Math Block |
---|
| q_0^2 = \frac{A^2}{c^* \rho^*} \cdot \frac{1 - (\rho/\rho_0)^2 \cdot \exp \left( -L/ L^* \right)}{2 \ln (\rho_0/\rho) + fL/d \cdot (1- \exp \left( - L/ L^* \right))/(L/L^*)} |
|
LaTeX Math Block |
---|
| c^* \, \rho^* = c _0 \, \rho_0 |
|
LaTeX Math Block |
---|
| L^* = c^* \, \rho^* \, G \, L |
|
LaTeX Math Block |
---|
| \rho/\rho_0 = \frac{1+ c^* p}{1+ c^* p_0} |
|
LaTeX Math Block |
---|
| \dot m^2 = \frac{A^2}{c^* \rho^*} \cdot \frac{\rho_0^2 - \rho^2 \cdot \exp \left( -L/ L^* \right)}{2 \ln (\rho_0/\rho) + fL/d \cdot (1- \exp \left( - L/ L^* \right))/(L/L^*)} |
|
LaTeX Math Block |
---|
| c^* \, \rho^* = c _0 \, \rho_0 |
|
LaTeX Math Block |
---|
| L^* = c^* \, \rho^* \, G \, L |
|
LaTeX Math Block |
---|
| \rho/\rho_0 = \frac{1+ c^* p}{1+ c^* p_0} |
|
LaTeX Math Block |
---|
anchor | static |
---|
alignment | left |
---|
| \dot m = A \cdot \sqrt{2 \, \rho^* (p_0 - p)} \cdot \sqrt{ \frac{1 + 0.5 \, c^* (p_0 + p)}{2 \ln \frac{1+c^*p_0}{1 + c^* p} + \frac{f \, L}{d}}} |
|
LaTeX Math Block |
---|
anchor | static |
---|
alignment | left |
---|
| \rho = \rho_0 \, \exp (c^* \rho^* \, G \, L) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{j_m^2}{G \, \rho_0^2} \cdot ( 1 - \exp(-2 \, c^* \rho^* \, G \, L))} |
|
LaTeX Math Block |
---|
anchor | static |
---|
alignment | left |
---|
| p(L) = \frac{1}{c^*} \cdot \left[
-1 + (1+c^* p_0) \cdot \exp (c^* \rho^* \, G \, L) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{j_m^2}{G \rho_0^2} \cdot \big(1 - \exp (-2 \, c^* \rho^* \, G \, L) \big) }
\right] |
|
Pressure Profile in GC-proxy static fluid column @model | LaTeX Math Inline |
---|
body | \dot m = 0, \, q_0 = 0 |
---|
|
(no flow) |
|
|
LaTeX Math Block |
---|
anchor | static |
---|
alignment | left |
---|
| p(L) = \frac{-1 + (1+c^* \, p_0) \cdot \exp(c^* \rho^* G \, L)}{c^*} |
|
See also
...