PROBLEM $2(25$ points$)$

Water at $)$

$u=(1\mathrm{.}307{10}^{-5}\frac{m^2}{s}$ is pumped from a lake, as illustrated below. The vapor pressure of water at this temperature is $1\mathrm{.}228$ kPa $.$ The flow rate through the pipe is $11\frac{L}{s}.$ Your task is to determine the maximum allowable length of the pipe section between the lake and the pump $($downstream of the pipe's entrance$)$ to prevent cavitation in the pump. The entrance loss coefficient for the pipe is $0\mathrm{.}80.$

HINT: The pressure at the lake's surface equals atmospheric pressure $(101$ kPa $),$ as the hydraulic design requires calculating the maximum pipe length that avoids cavitation within the pump.