Q$3$:

$(40$ Marks$)$

A vertical cylindrical tank $2m$ in diameter, is filled to a depth of $4m$ by a liquid of density $950k\frac{g}{m^3}$ and viscosity $7cP.$ It receives the liquid at a raie of $Q=0\mathrm{.}5\frac{m^3}{h}$ and drains through a horizontal tube, $4m$ long and $8mm$ in diameter, conected to its base. How does the liquid depth in the tank vary with time? Hagen$-$Poiseuille equation is $u=\frac{g{d}^{2}h}{32L}$

solve it on a paper with writing with clear handwriting "engineering and numerical analysis"