$*$QL$4.$ A liquid of density $1200$ kg$/$m$3$

flows from pipe A$,$ of diameter $50$ mm$,$ into pipe B$,$ of diameter $100$

mm$,$ through an abrupt expansion. A little way downstream of the expansion is a pitot tube facing the

oncoming flow; this is connected to end of a U$-$tube manometer containing mercury, density $13,600$ kg$/$m$3$

$.$

The other end of the manometer is connected to a static pressure tapping in the side of pipe A$.$ Calculate

the flow rate of the liquid if the difference in mercury levels is $50$ mm$.$