I meet one question that is very difficult although the answer is given!
Q. Water is stored in an elevated reservoir. To generate power, water flows from this reservoir down through a large conduit to a turbine and then through a similar-sized conduit. At a point in the conduit 89.5 m above the turbine, the pressure is 172.4 kPa, ans at a level 5 m below the turbine, the pressure is 89.6 kPa. The water flow rate is 0.800 m3/s. The output of the shaft of the turbine is 658 kW.The water density is 1000 kg/m3. If the efficiency of the turbine in converting the mechanical energy given up by the fluid to the turbine shaft is 89% (nt = 0.89), calculate the friction loss in the turbine in J/kg. Note that in the mechanical-energy balance equation, is equal to the output of the shaft of the turbine over nt. Ans. F = 85.3 J/kg
By Mechanical-energy balance equation,
(p2 - p1)/ρ + 1/2 (u2^2 - u1^2) + g(z2 - z1) - F = ntWp
-82.8 + 0 + 9.8 (5 - 89.5) - F = - 0.89 (658 x 10^3) / (1000 x 0.8 )
F = - 178.9 J/kg
What's wrong with my calculation?? Why it is equal to 85.3 J/kg in text book answer?