A pipeline ABC connects two pressurised tanks with absolute pressure

PA $=1\mathrm{.}50$ x $105$ Pa for tank A and PC $=1\mathrm{.}45$ x $105$ Pa for tank C$.$ The liquid

surface of the tank A is $3\mathrm{.}5$ m above the liquid surface of the tank C$.$ The pipe

leaves the top tank A at a depth of $1\mathrm{.}5$ m below its liquid surface. The pipe

extends for $140$ m horizontally before it reaches point B$.$ At point B there is a

smooth and shallow angled bend and the pipe slopes down and enters into tank

C below its free surface. The length of pipe from point B to the lower tank C is

$100$ m$,$ and the pipe diameter is $0\mathrm{.}15$ m throughout the system.

$($i$)$ Sketch a diagram of the piping system.

$($ii$)$ Using a Fanning friction factor of $0\mathrm{.}008$ determine the water flow rate at

point B$.$ You may neglect all energy degradation except that due to pipe

friction. The Darcy equation is:

$=4$

$$

$2$

$$

$$

$2$

$$

where the symbols have their usual meaning. The density and viscosity of

water are $1000$ kg m$-3$ and $0\mathrm{.}001$ Pa s$.$