p_r = \frac{1}{V} \int p(r) dV = \frac{2}{r_e^2} \int p(r) \, r \, dr = \frac{2}{r_e^2} \int \Biggbigg[ p_i - \frac{q_t}{2\pi \sigma} \ln \frac{r}{r_w} \Biggbigg] \, r \, dr = p_i - \frac{q_t}{2\pi \sigma} \Biggbigg[ 2 \ln \frac{r_e}{r_w} -1 \Biggbigg] |