Question $2$:

Water flows through a pipe that descends from section $1$ to section $2.$ The diameter at section $1$ is $0\mathrm{.}25$ m $,$ and the diameter at section $2$ is $0\mathrm{.}1$ m $.$ The height at section $1$ is $10$ m $,$ and at section $2,$ it is $5$ m $.$ The pressure at section $1$ is $300$ kPa $,$ and the pressure at section $2$ is $200$ kPa $.$ The density of water is $1000k\frac{g}{m^3}.$ Using Bernoulli's equation and the continuity equation, determine the velocities $U_1$ and $U_2$ at sections $1$ and $2,$ and calculate the volumetric flow rate $Q$ at the end. Assume that the flow is steady and incompressible, and neglect any friction losses.