Problem $2(10$ points$)$

A constant$-$head experiment $($figure below$)$ was conducted on a cylindrical column packed with a soil. The diameter of the soil column is $5cm.$ The column length is $L=30cm.$ The outflow rate $Q_{\text{o}\text{u}\text{t}}=30c\frac{m^3}{sec}$ was measured downstream. Water level from the upstream tank to the bottom of the soil column is $1\mathrm{.}0m.$ Water level difference between the upstream tank and downstream tank is $0\mathrm{.}6cm.$ Water has specific weight of $9810\frac{N}{m^3}$ and dynamic viscosity of $0\mathrm{.}0015N.\frac{s}{m^2}.$ Water flows from the bottom of the soil column $($cross section B$)$ to the top of the soil column $($cross section A$).$

$(1)$ Given this setup, calculate hydraulic head at cross section A and cross section B

$(2)$ Estimate intrinsic permeability of the soil $(r$