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Figure $6\mathrm{.}7$: The two connected reservoirs.

A uniform pipeline, $5168(L)m$ long, $212(D)mm$ in diameter, with a roughness $lon$ of $0\mathrm{.}031$

$mm,$ conveys water between two reservoirs, as shown in Figure $6\mathrm{.}7.$ The difference in water

level $H$ is maintained constant at $49m.$ The pipe is connected to the reservoirs with a sharp

edge. Along the pipe, there is a valve whose head loss coefficient $f_v$ is $11\mathrm{.}4.$ The viscosity of

the water is $0\mathrm{.}9*{10}^{-6}{m}^2{s}^{-1}.$ Determine the velocity of the flow in the pipe joining the two

reservoirs and draw the energy and hydraulic grade lines. Of the three schematics shown in

Figure $6\mathrm{.}8,$ wich is realistic $($the top, the middle or the bottom$)?$

Hint: Write the energy balance including major and minor losses. Since you do not know

the velocity, you do not know the Reynolds number. You also do not know $f.$ Guess a value

of $f($or the velocity$)$ and calculate the velocity $($or $f)$ from the energy balance. Calculate $Re$

and use either the Moody diagram or the Colebrook$-$White formula to calculate a new value

of $f.$ Repeat until the procedure converges to a single value.