Orlík hydroelectric plant

The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power.
a) What is the total installed power of the power plant at efficiency n = 87%?
b) For the fast charging of electric vehicles overnight, power consumption up to P0 = 11kW is required. How many would electric cars cover power plant power?
c) How many days of full power operation corresponds to the delivered energy E = 398GWh

Result

P =  361.018 MW
n =  32820
d =  45.9

Solution:

h=70.5 m Q=150 m3/s p=87/100=87100=0.87 n=4 g=9.81 m/s2 w=1000 kg/m3  E=m⋅ g⋅ h P1=Q⋅ w⋅ g⋅ h=150⋅ 1000⋅ 9.81⋅ 70.5=103740750 W P11=P1/106=103740750/106≐103.7408 MW P=p⋅ n⋅ P11=0.87⋅ 4⋅ 103.7408≐361.0178≐361.018 MWh=70.5 \ \text{m} \ \\ Q=150 \ \text{m}^3\text{/s} \ \\ p=87/100=\dfrac{ 87 }{ 100 }=0.87 \ \\ n=4 \ \\ g=9.81 \ \text{m/s}^2 \ \\ w=1000 \ \text{kg/m}^3 \ \\ \ \\ E=m \cdot \ g \cdot \ h \ \\ P_{1}=Q \cdot \ w \cdot \ g \cdot \ h=150 \cdot \ 1000 \cdot \ 9.81 \cdot \ 70.5=103740750 \ \text{W} \ \\ P_{11}=P_{1}/10^6=103740750/10^6 \doteq 103.7408 \ \text{MW} \ \\ P=p \cdot \ n \cdot \ P_{11}=0.87 \cdot \ 4 \cdot \ 103.7408 \doteq 361.0178 \doteq 361.018 \ \text{MW}
P0=11/1000=111000=0.011 MW n=P/P0=361.0178/0.011≐32819.8182≐32820P_{0}=11/1000=\dfrac{ 11 }{ 1000 }=0.011 \ \text{MW} \ \\ n=P/ P_{0}=361.0178/ 0.011 \doteq 32819.8182 \doteq 32820
E=398 GWh  P2=P/1000=361.0178/1000≐0.361 GW d=E/(24⋅ P2)=398/(24⋅ 0.361)≐45.9349≐45.9E=398 \ \text{GWh} \ \\ \ \\ P_{2}=P/1000=361.0178/1000 \doteq 0.361 \ \text{GW} \ \\ d=E/(24 \cdot \ P_{2})=398/(24 \cdot \ 0.361) \doteq 45.9349 \doteq 45.9

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