Question $5$: Pipe with a contraction, find velocity

Water flows at steady state through a horizontal pipe with a contraction. The water has constant$-$density $=1000k\frac{g}{m^3}.$ The pipe

has a circular cross section which changes from radius $R_1=0\mathrm{.}2m$ to radius $R_2=0\mathrm{.}1m.$ Along the streamline from $1$ to $2,$ the

pressure decreases from $P_1=201Pa$ to $P_2=86Pa.$ Velocity is approximately uniform across the wide cross$-$section. Velocity is

approximately uniform across the narrow cross$-$section, with a value of $U_2=0\mathrm{.}4\frac{m}{s}.$ The flow of air outside of the pipe is weak,

such that wind shear on the sides of the control volume can be neglected. The loss coefficient in the contraction is not known.

Calculate $U_1,$ the average velocity in the wide cross$-$section.

$U_1$