A circular water pipe has an abrupt expansion from diameter D₁= 8 cm to D₂= 24 cm. The pressure and the average water velocity in the smaller pipe are P₁= 135 kPa and 10 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 momentumflux correction factors, show that the loss coefficient for sudden expansion is K_L= (1 - D₁²/D₂²)², and calculate K_Land P₂for the given case.

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D2 V= 10 m/s