Answer:
11.87 ft
Explanation:
Volumetric flow rate of the turbine Q = 1.7 million gal/min
Q = 1.7 x [tex]10^{6}[/tex] gal/min
1 gal = 0.00378541 m^3
1 min = 60 sec
1.7 x [tex]10^{6}[/tex] gal/min = (1.7 x [tex]10^{6}[/tex] x 0.00378541)/60 = 107.25 m^3
average velocity of flow through turbine = 34 ft/s
1 ft = 0.3048 m
34 ft/s = 34 x 0.3048 = 10.36 m/s
According to continuity equation, Q = AV
where Q = volumetric flow rate
A = Area of conduit
V = velocity of flow through turbine
A = Q/V = 107.25/10.36 = 10.35 m^2
Area of conduit = [tex]\pi r ^{2}[/tex]
radius r = [tex]\sqrt{\frac{area}{\pi } }[/tex] = [tex]\sqrt{\frac{10.35}{3.142} }[/tex] = 1.81 m
diameter = 2 x radius = 2 x 1.81 = 3.62 m
diameter = 3.62 m = 3.62 x 3.28084 = 11.87 ft
