1 In a certain municipality, they want to set up a hydroelectric power plant, and for this purpose, they wish to utilize the energy of the water flowing at the border. Preliminary calculations are to be made to determine how many light bulbs the water's energy can power in the case of the lowest water level. The river flows in a rectangular parallelogram-shaped channel at one point, which is $5 \mathrm{~m}$ wide. Even at the lowest water level, the depth of the water is $0.9 \mathrm{~m}$. The speed of the water was determined using a floating piece of wood and it was found that it covers a distance of $70 \mathrm{~m}$ in 100 seconds. The terrain conditions are such that a drop of $3 \mathrm{~m}$ can be easily established. The turbines and associated generators convert $80 \%$ of the available energy into electrical energy, and $10 \%$ of the energy is lost in the transmission lines. A 16 standard candlepower lamp in a carbon filament operates at 110 Volts and 0.5 Amperes.[^0]


[^0]:    1* We also gladly accept solutions to starred problems from university students.
The volume of water flowing per second:

$$
\frac{5 \cdot 0.9 \times 70}{100} \mathrm{~m}^{3}=3.15 \mathrm{~m}^{3}=3150 \mathrm{dm}^{3}
$$

The weight of this volume is $=3150 \mathrm{~kg}$.

The work done by the force of gravity:

$$
3 \cdot 3150 \mathrm{~m} \mathrm{~kg}=9450 \mathrm{~m} \mathrm{~kg}=9450 \times 9.81 \text { joule }=92704.5 \text { joule. }
$$

This amount of energy is available per second. However, only $80 \%$ of it can be converted into electrical energy, which is 74163.6 joules. Thus, a dynamo of at least this power can be supplied by such a water flow, with a capacity of

$$
74163.6 \text { watts. }
$$

But $10 \%$ of the electrical energy is lost in the wires, leaving

$$
66747.2 \text { watts. }
$$

for lighting. A lamp consumes

$$
110 \times 0.5 \text { volt-ampere }=55 \text { watts }
$$

and thus $\frac{66747.2}{55}=1214$ lamps can be connected to operate at full intensity.

(Bartók Imre, Budapest.)

The problem was also solved by: Aczél F., Bayer B, Póka Gy., Szmodics K., Tóbiás J.L.