As a design engineer, you have been asked

to provide piping schematics for a reverse

osmosis desalination plant. One

specification in your design calls for a

straight section of steel pipe $($with a surface

roughness $$ of $0\mathrm{.}002mm)$ to deliver $139\frac{L}{s}$

of salt water for a horizontal distance of $24$

$m.$ You assume the salt water has a density

of $1,020k\frac{g}{m^3}$ and a kinematic viscosity

$u$

of $1\mathrm{.}62{10}^{-6}\frac{m^2}{s}.$ Since the pumps are

already working hard to produce the fresh

water, you limit the allowable major head

loss in this section to $0\mathrm{.}15m.$ Use the

Swamee$-$Jain correlation to determine the

minimum allowable diameter of the pipe in

m$.$ Provide your answer to $3$ decimal places.