$1.($from Nash, $2003)$ A study on an isotropic, homogeneous confined aquifer shows the water elevation in three piezometers as indicated in the map below. With the information provided determine $($all dimensions are in meters. Show all your calculations; $15$ points$)$:

a$.$ The gradient of the piezometric surface

b$.$ Construct the piezometric surface map $($isolines every $20$ meters$)$

c$.$ The direction of water flow