Answer:
62.1 ft
Explanation:
We know that [tex]1 gpm= 0.0022 ft^{3}/s[/tex] hence 240 gpm will be
[tex]240*0.0022=0.528 ft^{3}/s[/tex]
From the formula of obtaining efficiency
[tex]\eta=\frac {\gamma Q h_a}{500W_{in}}[/tex] and making [tex]h_a[/tex] the subject we have
[tex]h_a=\frac {\eta*550*W_{in}}{\gamma Q}[/tex] where Q is flow rate, [tex]\gamma[/tex] is specific weight of water, [tex]h_a[/tex] is actual head rise and [tex]W_{in}[/tex] is the power input to the compressor
Substituting 0.62 for [tex]\eta[/tex], 6hp for [tex]W_{in}[/tex], [tex]62.4 lb/ft^{3}[/tex] for [tex]\gamma[/tex] and [tex]0.528 ft^{3}/s[/tex] for Q then
[tex]h_a=\frac {0.62*550*6}{62.4*0.528}=\frac {2046}{32.9472}=62.09936\approx 62.1 ft[/tex]
Therefore, actual head rise of the water being pumped is 62.1 ft
