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titleDerivation


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p_rV = \frac{1}{V} \int p(r)pi r_e^2 h, \quad dV = 2\frac{1}{\pi r \, r_e^2 h}, dr 


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p_r = \frac{1}{V} \int p(r) dV\int p(r) 2 \pi \, r \, h \, dr = \frac{2}{r_e^2} \int p(r) \, r \, dr


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p_r = \frac{2}{r_e^2} \int \Bigg[ p_i - \frac{q_t}{2\pi \sigma} \ln \frac{r}{r_w} \Bigg] \, r \, dr = p_i - \frac{q_t}{2\pi \sigma} \Bigg[ 2 \ln \frac{r}{r_w} -1 \Bigg]


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