changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Mar 23, 2019
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\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_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(r_w ) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w}
r_{wf} \leq r \leq r_e
p(r) = p_i + \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_e} = p_{wf} - \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_w}
p_{wf} = p_i - \frac{q_t}{2 \pi \sigma} \, \bigg[ S + \ln \frac{r_e}{r_w} \bigg]
