Question

Lake Arenal is a lake which is situated in the northern highlands of Costa Rica. It is currently the largest lake in Costa Rica at 85-square-kilometre surface area. Its depth average is 45 meters.

Every hour, 0.2%. of the lake’s volume can be dropped through a vertical height of 50 m and pass thrrough a turbine and produce electricity with an efficiency of 90% What is the electrical power output (in MW) of this facility?

Answer 1

Volume of lake = 85×10^6m^2 *. 45m

= 3.825×10^9 m^3

0.2% of total volume = 0.2 ×3.825×10^9/100

= 7.65×10^6 m^3

Mass falling in1 hr

=1000 kg/m^3 * 7.65×10^6m^3

= 7.65×10^9 kg

Decrease in gravitational potential energy of mass m when dropped through height h

= mgh

Decrease in gravitational potential energy

= 7.65×10^9 kg*9.81m/s^2*50m

= 3.75×10^12 J

90% of this energy = 3.38×10^12J

This is electrical energy generated in one hr.

Electrical energy generated per second

= 3.38×10^12J/hr / 3600 sec/hr

= 9.4×10^8 W = 9.64×10^2 MW