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 entire power operation corresponds to the delivered energy E = 398GWh

Correct answer:

P =  361.0178 MW
n =  32820
d =  45.9

Step-by-step explanation:

$$\begin{gathered} h=70.5\text{m} \\ Q=150{\text{m}}^3\text{/s} \\ p=87\%=\frac{87}{100}=0.87 \\ n=4 \\ g=9.81{\text{m/s}}^2 \\ w=1000{\text{kg/m}}^3 \\ E=m\cdot g\cdot h \\ {P}_1=Q\cdot w\cdot g\cdot h=150\cdot 1000\cdot 9.81\cdot 70.5=103740750\text{W} \\ {P}_{11}=P_1/10^6=103740750/10^6\doteq 103.7408\text{MW} \\ P=p\cdot n\cdot P_{11}=0.87\cdot 4\cdot 103.7408=361.0178\text{MW} \end{gathered}$$

$$\begin{gathered} P_0=11/1000=\frac{11}{1000}=0.011\text{MW} \\ n=P/P_0=361.0178/0.011=32820 \end{gathered}$$

$$\begin{gathered} E=398\text{GWh} \\ {P}_2=P/1000=361.0178/1000\doteq 0.361\text{GW} \\ d=E/(24\cdot P_2)=398/(24\cdot 0.361)=45.9 \end{gathered}$$

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