$4.$ Two elevated tanks supply water to a demand node with a valve at its outlet $($Figure $2).$ The elevated tanks are cylindrical and have diameters of $5$ m $.$ The initial water level in Tank $1$ is $96$ m and the initial water level in Tank $2$ is $91$ m $.$ The valve is half open and has a discharge coefficient of $\backslash (0\mathrm{.}15\backslash$mathrm$\{$~m$\}^\{5/2\}/\backslash$mathrm$\{$s$\}\backslash ).$ The initial steady$-$state flow through the valve is $\backslash (350\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The valve discharges to the atmosphere. Both pipes have a Hazen$-$Williams $\text{'}\backslash ($ C $\backslash )\text{'}$ factor of $100,$ an internal diameter of $300$ mm $,$ and a length of $350$ m $.$ Assuming quasi$-$steady conditions in the system, determine the pressure head at the demand node and the flow in the pipes in the first three time steps of the simulation. Use a time step of $15$ seconds to carry out the quasi$-$steady state simulation.

'Figure $2.$ Water supply system.