Question 2 of 10 Sapling Learning macmillan loaming One method used to store ene

Question

Question 2 of 10 Sapling Learning macmillan loaming One method used to store energy during times of low demand is by pumping water uphill into a reservoir When energy demand exceeds the output produced by power plants, the water is released, moves downhill and is converted into electricity by a turbine During a 151.0 minute long period of low usage, 61.0 MW is used to pump water up an elevation of 77.5 m in a series of 1.00 m diameter pipes. The friction loss in the pipe going to the upper reservoir is 41.3 m /s What is the mass flow rate, m of water during the low usage period? Number kg/s What is the total mass of water raised 77.5 m during this 151.0 minute period? Number kg How long can the turbines produce 300.0 MW of power from the release of the mass of stored water calculated above? Assume the water sustains a friction loss of 41.3 m2/s2 on the way down to the turbine Number min

Explanation / Answer

(1)

P= dM/dT(g*h+41.3)

61*10*6=dM/dT(9.8 x 77.5 +41.3 )

dm/dt=76.17 *10^3 kg/sec

(2)

Total mass=Time x dm/dt

= 151 min * 60 s /min *76.17 *10^3 kg/sec
Total mass=6.9*10^8 kg

(3)

300*10*6 = dm/dt (77.5 *9.8 - 41.3)
dm/dt = 4.177*10^5 kg/sec

Time = total mass/4.177*10^5

= 6.9*10^8 kg/4.177*10^5

=1651.9 sec

=27.53 min
(4)

Efficiency=(77.5*9.8 - 41.3)/(77.5*9.8 + 41.3 )

=0.90

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