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Note
titleDisclaimer

It is important to note that equations

LaTeX Math Block Reference
anchorE1
LaTeX Math Block Reference
anchorE4
do not constitute a complete CVP as it does not specify the initial condition.


Expand
titleSolution



LaTeX Math Block
anchorpwf
alignmentleft
p(t,r) = p_i - \frac{{\rm w \,}  q_t }{V_e \, \phi \, c_t} \, t + \frac{{\rm w \,} q_t }{4\pi \sigma} \left[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_e^2} + 1 \right] 
 , \quad r_{wf} < r \leq r_e, 
\quad {\rm w }= 1 - \frac{r_w^2}{r_e^2}




LaTeX Math Block
anchorpwf
alignmentleft
p_e(t) = p_i - \frac{{\rm w \,} q_t}{V_e \phi c_t}t





LaTeX Math Block
anchorpwf
alignmentleft
p_{wf}(t) = p_e(t) - \frac{q_t}{2 \pi \sigma} \, \left[ {\rm w\, } \ln \frac{r_e}{r_w}  + 0.5 + S \right]



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