Water is pumped at a rate of $500 mathrm{gpm}$ through a $10 mathrm{in}$. ID pipeline, $50 mathrm{ft}$

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Water is pumped at a rate of $500 \mathrm{gpm}$ through a $10 \mathrm{in}$. ID pipeline, $50 \mathrm{ft}$ long, with both entrance and exit from the pipe at ground level. The line contains two standard elbows and a swing check valve. The pressure is $1 \mathrm{~atm}$ entering and leaving the pipeline. Calculate the pressure drop (in psi) through the pipeline due to friction using (a) the $2-K$ method, (b) the ( $L / D)_{e q}$ method, and (c) the 3-K method.

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