Question

Water flows from the bottom of a large tank where the pressure is 100 psig through a pipe to a turbine which produces 5.82 hp. The pipe leading from the turbine is 60 ft below the bottom of the tank. In this pipe the pressure is 50psig, the velocity 70 ft/, and the flow rate 100 lb/s. If the friction loss in the system, excluding the turbine, is 40 ft*Ib/Ibm, find the efficiency of the turbine.

Answer 1

Explanation:

Bernoulli equation for the flow between bottom of the tank and pipe exit point is as follows.

   $\frac{p_{1}}{\gamma} + \frac{V^{2}_{1}}{2g} + z_{1}$ = $\frac{p_{2}}{\gamma} + \frac{V^{2}_{2}}{2g} + z_{2} + h_{f} + h_{t}$

    $\frac{(100 \times 144)}{62.43} + 0 + h[tex] = [tex]\frac{(50 \times 144)}{(62.43)} + \frac{(70)^{2}}{2(32.2)} + 0 + 40 + 60$

                          h = $\frac{(50 \times 144)}{(62.43)} + \frac{(70)^{2}}{2(32.2)} + 40 + 60 - \frac{(100 \times 144)}{(62.43)}$

                            = 60.76 ft

Hence, formula to calculate theoretical power produced by the turbine is as follows.

                                 P = mgh

                                     = $100 \times 60.76$

                                     = 6076 lb.ft/s

                                     = 11.047 hp

Efficiency of the turbine will be as follows.

                $\eta_{t}$ = $\frac{P_{actual}}{P_{theoretical}}$ × 100%

                                = $\frac{5.82}{11.047} \times 100%$                      

                                = 52.684%

Thus, we can conclude that the efficiency of the turbine is 52.684%.