QUESTION $2$

Problem $2$: Cooling System Design for a Data Center the data center receive adequate cooling.

Given:

The pipes are made of smooth steel, and the water is pumped through them at a total flow rate of $Q=0\mathrm{.}02m\frac{3}{s}$

Find:

Flow Distribution: Determine the flow rate through each pipe using the continuity equation and the principle that the head loss must be the same across all four pipes.

Friction Factor Calculation:

Calculate the Reynolds number for each pipe using the flow rate obtained

Use the Haaland equation to find the friction factor for each pipe:

$\frac{1}{\sqrt[\phantom{2}]{7}}=-1\mathrm{.}8log[(\frac{\frac{c}{D}}{3\mathrm{.}7}{)}^{1\mathrm{.}11}+\frac{6\mathrm{.}9}{Re}]$

Assume the relative roughness $($e$/$D$)$ is negligible for smooth pipes.

$3.$ Head loss: Calculate the head loss $($pressure drop$)$ across each pipe and verify that they are equal, ensuring proper flow distribution.

$h_f=f*\frac{L}{D}*\frac{v^2}{2g}$

Additional Information:

Density of water: $=1000k\frac{g}{m^3}$

Viscosity of water: $=0\mathrm{.}001Pa*s$

Relative roughness:e $=0\mathrm{.}00003m$

Here you will find the data for question $2.$ Use this data to solve the problem and upload the result to $8$ B

$D1=0\mathrm{.}136,D2=0\mathrm{.}225$ all diameters in m

$L1=145,L=387$ all length in m