$(20)$ A drip coffee maker has a basket for grounds that is ${4\mathrm{.}5}^{\text{'}\text{'}}$ in diameter. When making ten $6oz$ cups of coffee, ground coffee is added to the basket to a height of $3\mathrm{.}5".$

a$.$ If $0\mathrm{.}2"$ of water sits on top of the ground coffee during the entire brew process, what hydraulic pressure is exerted on the coffee grounds by the water?

b$.$ Calculate the rate $(m\frac{l}{m}in$ at which water is permeating through the coffee grounds if all of the water has passed through the grounds in $4\frac{1}{2}$min.

c$.$ Assume the water flowing through coffee grounds obeys Darcy's law; calculate the resistance of the coffee grounds to water flow.

d$.$ What is the permeability constant for the coffee grounds $(c{m}^2)?$