I need help with question a and b$.$

Use Darcy$$s Law to derive an equation for the volumetric flow rate $($Qv$)$ through a porous

sphere. The sphere has a radius Re and a hollow core with radius Ri$.$ A cross$-$section of

the sphere is provided below. Assume that the pressure inside the sphere $($Pi$)$ is greater

than the pressure outside the sphere $($Pe$),$ thus driving the flow outward radially.Consider the "Moka Coffee Pot" discussed in lecture, where water is heated in an air$-$tight

chamber and the subsequent build$-$up of pressure forces water up through the coffee

grounds. Coffee grounds are packed into the system as a cylindrical puck with diameter,

$D=10cm,$ and height, $h=2cm.$ Assuming the gas in the chamber behaves ideally:

a$.$ What is the new pressure, $P_2,$ inside of the air$-$tight chamber after heating the

system from $20C$ to $90C?$ Assume the initial pressure inside the chamber, $P_1,$ is

equal to $1$atm, the same as the external pressure. You may neglect volume

changes and water evaporation.

b$.$ Use Darcy's Law to calculate the initial volumetric flow rate $(Q_v)$ through the coffee

grounds at the elevated temperature. Assume a permeability $k=2\mathrm{.}3{10}^{-8}c{m}^2.$ In

your calculations, use the appropriate physical properties for water at $90C.$ Report

$Q_v$ in units of $\frac{L}{m}in.$