a$.)$ A pump test in an unconfined permeable layer is carried out as shown in Figure $5\mathrm{.}1.$ Show that the equation for $k$ is $($read section $7\mathrm{.}11)$

$k=\frac{2\mathrm{.}303qlo{g}_{10}(\frac{r_1}{r_2})}{(h_1^2-h_2^2)}$

b$.)$ while A pump test is carried out to determine the hydraulic conductivity of a confin aquifer, as shown in Figure $5\mathrm{.}2,$ Show that the equation for $k$ is:

$k=\frac{qlo{g}_{10}(\frac{r_1}{r_2})}{2\mathrm{.}727H(h_1-h_2)},k=\frac{qln(\frac{r_1}{r_2})}{2H(h_1-h_2)}$