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If capillary effects are not high
or saturation does not vary along the streamline substantially
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| body | \displaystyle \frac{\partial s_w}{\partial r} \rightarrow 0 |
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, then
| LaTeX Math Inline |
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| body | \displaystyle \frac{\partial P_c}{\partial r} = \dot P_c \cdot \frac{\partial s_w}{\partial r} \approx 0 |
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.
If flow is close to horizontal horizontal
| LaTeX Math Inline |
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| body | \sin \alpha \rightarrow 0 |
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then gravity effects are vanishing too
and : | LaTeX Math Inline |
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| body | (\rho_w-\rho_o) \cdot g \cdot \sin \alpha \approx 0 |
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.
In these cases
| LaTeX Math Block Reference |
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simplifies to:
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