Water flows through a pipe as shown in the figure. The pressure at points $1$ and $2$ respectively is $1\mathrm{.}90105$ Pa and $1\mathrm{.}20105$ Pa$.$ The radius of the pipe at points $1$ and $2$ respectively is $4\mathrm{.}00$ cm and $1\mathrm{.}50$ cm$.$ If the vertical distance between points $1$ and $2$ is $2\mathrm{.}75$ m$,$ determine the following.

$($a$)$ speed of flow at point $1$

$($b$)$ speed of flow at point $2$

$($c$)$ volume flow rate of the fluid through the pipe