Answer
$1.96\times10^{-2}\;m^3/s$
Work Step by Step
From part $(a)$, we have obtained
$V=\sqrt {\frac{2a^2\Delta p}{\rho(a^2-A^2)}}$
or, $V=\sqrt {\frac{2a^2(p_2-p_1)}{\rho(a^2-A^2)}}$
Therefore, the rate of water flow is given by
$R=AV$
or, $R=A\sqrt {\frac{2a^2(p_2-p_1)}{\rho(a^2-A^2)}}$
Substituting the given values
$R=64\times10^{-4}\times\sqrt {\frac{2\times32^2\times(41-55)\times10^{3}}{1000\times(32^2-64^2)}}\;m^3/s$
or, $\boxed{R=1.96\times10^{-2}\;m^3/s}$
