Question

6. Determine the power required for a 5000-kg car to accelerate from 5m/s to 20m/s in 10 seconds. (Show the formula and procedures.) 7. For a hydroelectric plant, a hydraulic turbine-generator is installed at the site below the free surface. The turbine drives a generator for electricity. The elevation difference between the two free surfaces is h = 60m. The mass flow rate of water is th = 300kg/s. The shaft power output from the turbine is W. = 87kW. 1) What is the power input to the turbine from the fluid tuld? 2) What is turbine ? 3) If generator = 89%, what is the overall efficiency of the whole plant turbine-generator? (g = 9.81m/s2)

Answer 1

Given: mass (m) = 5000 kg Initial velocity (V, ) = 5 m/s Final velocity (V₂) = 20m/s. time (t) = 10 sec. Force (F) = mass (m) x acceleration (a) acceleration (a) = Final velocity - Initial velocity Change in time F = 5000 (205) = 5000 x 150 = 7500 N Distance covered (s) = vt itt at S=5x10 + 2 x (20-15) (10) - 125m workdone = Force (FX displacement (s) 7500 x 125 = 937500 Nm Power - workdone time = 937500 = 93750 Nm = 93.750kW

Hence, the power required for 5000 kg car to accelerate from 5 m/s to 20 m/s in 10 seconds was found to be 93.750 KW.