Respuesta :
Explanation:
Bernoulli equation for the flow between bottom of the tank and pipe exit point is as follows.
[tex]\frac{p_{1}}{\gamma} + \frac{V^{2}_{1}}{2g} + z_{1}[/tex] = [tex]\frac{p_{2}}{\gamma} + \frac{V^{2}_{2}}{2g} + z_{2} + h_{f} + h_{t}[/tex]
[tex]\frac{(100 \times 144)}{62.43} + 0 + h[tex] = [tex]\frac{(50 \times 144)}{(62.43)} + \frac{(70)^{2}}{2(32.2)} + 0 + 40 + 60[/tex]
h = [tex]\frac{(50 \times 144)}{(62.43)} + \frac{(70)^{2}}{2(32.2)} + 40 + 60 - \frac{(100 \times 144)}{(62.43)}[/tex]
= 60.76 ft
Hence, formula to calculate theoretical power produced by the turbine is as follows.
P = mgh
= [tex]100 \times 60.76[/tex]
= 6076 lb.ft/s
= 11.047 hp
Efficiency of the turbine will be as follows.
[tex]\eta_{t}[/tex] = [tex]\frac{P_{actual}}{P_{theoretical}}[/tex] × 100%
= [tex]\frac{5.82}{11.047} \times 100%[/tex]
= 52.684%
Thus, we can conclude that the efficiency of the turbine is 52.684%.
