Problem $1$:

$2\mathrm{.}31.$ A $50-mm$ diameter pipeline made of copper$-$tubing is connected directly to the water main as shown in Figure $2\mathrm{.}34.$ The pressure in the water main at Point $1$ is $400$kPa and the faucet of interest is at Point $6,$ which is $15\mathrm{.}0m$ vertically above the water$-$main connection. The length of pipeline from the water main to the faucet is $30\mathrm{.}0m,$ and the pipeline has the following characteristics:

$\backslash$table$[[$Location$,$Type of fixture$],[1,$sharp$-$edged entrance$],[2,3,5,90$ elbow$],[4,$tee$],[6,$globe valve$]]$

The is no flow in the line from Point $4$ to Point $7.$ According to the manufacturer of the faucet $(=$ globe valve$)$ the local$-$loss coefficient is equal to $4\mathrm{.}0$ when the faucet is fully open. In this case, the copper tubing is so smooth that the roughness height can be taken as zero. Estimate the flow rate in the pipeline when the faucet is fully open.

Solution: