changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Mar 23, 2019
...
\frac{\partial p}{\partial t} = 0 \Leftrightarrow \, \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} =0
p(t, r \rightarrow \infty_e ) = p_i
\left[ r\frac{\partial p(t, r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma}
p
_{wf} = p_i - \frac{q_t}{
2 \pi \sigma} \, \bigg[ S + \ln \frac{r_e}{r_w} \bigg]
p_{wf} = J =\frac{q_t}{p_i - p_{wf}}= \frac{q_t}{42 \pi \sigma} \, \bigg[ - 2S + {\ln \frac{r_e}{r_w} + \bigg]S} = {\rm const}
