In a metal processing plant which is operating at $1000K,$ a molten Aluminium with a

density of $2$

g$.$cm $3$ is flowing inside a temperature resistant cylindrical ceramic pipe.

The cross$-$section of the pipe $1$ is twice of the cross$-$section of pipe $2.$ The velocity

and the pressure of the molten metal inside the pipe $1$ is $0\mathrm{.}75\frac{m}{s}$ and $150$kPa,

respectively. By assuming that the molten metal is an incompressible fluid, determine:

$($a$).$ the pressure inside the pipe $2$

$($b$).$ the velocity along the pipe $2$

$($c$).$ the ratio of Reynolds numbers between wider to narrower pipes $($if the viscosity

of the molten Aluminium is $1\mathrm{.}2$mPa.$s)$