Homework $6$ MANE $2720$ Fluid Mechanics

Problem $26.(20$ Points$)$ A circular water pipe has an abrupt expansion from diameter $D_1=8cm$ to $D_2=24cm.$ The pressure and the average water velocity in the smaller pipe are $P_1=135$kPa and $10\frac{m}{s},$ respectively, and the flow is turbulent. By applying the continuity, momentum, and energy equations and disregarding the effects of the kinetic energy and momentum$-$flux correction factors, show that the loss coefficient for sudden expansion is $K_L=(1-\frac{D_1^2}{D_2^2}{)}^2,$ and calculate $K_L$ and $P_2$ for the given case.