(Solved): As shown in the figure below, the velocity of water v(m/s ...

As shown in the figure below, the velocity of water $v(\mathrm{m}/\mathrm{s})$, discharged from a cylindrical tank through a long pipe can be computed as: $v=\sqrt{2gH}\tanh \left(\sqrt{\frac{2gH}{2L}}t\right)$ Eq. 1.1 where $g=9.81\mathrm{m}/{\mathrm{s}}^2,\mathrm{H}=$ initial head $(\mathrm{m}),\mathrm{L}=$ pipe length $(\mathrm{m})$, and $t=$ elapsed time $(\mathbf{s})$. And water flow rate through a pipe can be calculated with: $Q=\frac{V}{t}=\frac{Ad}{t}=A\stackrel{?}{v}$ Eq. 1.2 where $\mathbf{Q}$ is flowrate in ${\mathrm{m}}^3/\mathrm{s},\mathbf{A}$ is the pipe coss-sectional area in $m^2$ and $\mathbf{v}$ is the water velocity in $\mathrm{m}/\mathrm{s}$. (a) plot the velocity function from Eq.1.1 for $H=0\mathrm{m}$ to $4\mathrm{m}$ (in increments of $1\mathrm{m}$ ), over time $t=0$ to 2.5 s and arbitrarily assigned pipe length $L$ between $2.0\mathrm{m}$ and $4.0\mathrm{m}$. Make sure to label to plot. For example: (b) plot the water acoeleration a based on the velocity function of Eq.1.1 for $\mathrm{H}=0\mathrm{m}$ to $4\mathrm{m}$ (in hwrements of im) and over time $t=0$ to 2.5 s (keep using the same $\mathrm{L}$ as before). Make sure to labed to phot For example: (c) using modular programming create a uniform flow rate branching water network simulation (segment $\mathrm{A}$ is directly fed with the water tank) for each $\mathrm{H}=0\mathrm{m}$ to $4\mathrm{m}$ ) by generating a branching water network with the following parameters: - one $50\mathrm{mm}$ feeder pipe (A) - two $32\mathrm{mm}$ primary distribution pipes (B) - four to eight (choose one even amount) $20\mathrm{mm}$ secondary distribution pipes (C) - fourty to eighty (choose one even tens amount) $10\mathrm{mm}$ end-point pipes (D) Uniform branched water network architecture Using modular programming create functions for: (i) pipe_velocity(): calculating the water velocity $v(\mathrm{m}/\mathrm{s})$ of a given pipe diameter $d(\mathrm{mm})$ and water flow rate $\mathbf{Q}\left({\mathrm{m}}^3/\mathrm{s}\right)$. Refer to Eq. 1.2 . (ii) pipe_flow_rate(): calculating the water flow rate $Q\left({\mathrm{m}}^3/\mathrm{s}\right)$ of a given pipe diameter $\mathrm{d}(\mathrm{mm})$ and water velocity $\mathbf{v}(\mathrm{m}/\mathrm{s})$. Refer to Eq. 1.2 . (iii) pipe_diameter(): calculating the pipe diameter $d(\mathrm{mm})$ of a given water velocity $v(\mathrm{m}/\mathrm{s})$ and flow rate $\mathbf{Q}\left({\mathrm{m}}^3/\mathrm{s}\right)$. Refer to Eq. 1.2 . (iv) pipe_volume(): calculating the pipe water volume per meter (litres/m) for a given pipe Uniform branched water network architecture Using modular programming create functions for: (i) pipe_velocity(): calculating the water velocity $v(\mathrm{m}/\mathrm{s})$ of a given pipe diameter $d(\mathrm{mm})$ and water flow rate $\mathbf{Q}\left({\mathrm{m}}^3/\mathrm{s}\right)$. Refer to Eq. 1.2. (ii) pipe_flow_rate(): calculating the water flow rate $Q\left({\mathrm{m}}^3/\mathrm{s}\right)$ of a given pipe diameter $\mathbf{d}(\mathrm{mm})$ and water velocity $v(\mathrm{m}/\mathrm{s})$. Refer to $\mathrm{Eq}.1.2$. (iii) pipe_diameter(): calculating the pipe diameter $d(\mathrm{mm})$ of a given water velocity $\mathbf{v}(\mathrm{m}/\mathrm{s})$ and flow rate $\mathbf{Q}\left({\mathrm{m}}^3/\mathrm{s}\right)$. Refer to Eq. 1.2 . (iv) pipe_volume(): calculating the pipe water volume per meter (litres/m) for a given pipe diameter $(\mathrm{mm})$. (v) vel_change(): calculating the outlet water velocity $v_{?}o(\mathrm{m}/\mathrm{s})$ of a given outlet pipe diameter d_o $(\mathrm{mm})$ that is fed from a given inlet pipe diameter ${\mathbf{d}}_{?}\mathbf{i}(\mathrm{mm})$ with a given water velocity $v_{?}i(\mathrm{m}/\mathrm{s})$. Assume that the inlet water flow rate and the outlet water flow rate are equal. Every pipe segment (A/B/C/D) must be represented with a data structure that stores the following information (use your functions to calculate the relevant info where possible): - pipe diarneter (mm). - water velocities (for each height of $\mathrm{H}=0\mathrm{m}$ to $4\mathrm{m}$ ) in the pipe $(\mathrm{m}/\mathrm{s})$. - water flow rates (for each height of $H=0\mathrm{m}$ to $4\mathrm{m}$ ) in the pipe $\left({\mathrm{m}}^3/\mathrm{s}\right)$. - water volume in pipe per meter (litres/m). - amount of these segments in the total branching water network. For example: (d) plot the water velocity in each pipe segment for $\mathrm{H}=0\mathrm{m}$ to $4\mathrm{m}$ (in increments of $1\mathrm{m}$ ) and over pipe diameters $10\mathrm{mm},20\mathrm{mm},32\mathrm{mm}$ and $50\mathrm{mm}$. Make sure to label the plot. For example: (e) discuss the results you obtained in your own words (one to two paragraphs)