Page 308 - Managing Global Warming

268 Managing Global Warming

The runoff regime (amount and variability of flow) depends on the local climate;
first of all on precipitation, air temperature, and potential evaporation, but also on the
properties of the catchment; soil type, topography, vegetation, and land use. In most
rivers, runoff shows considerable variability in time, both in the short range (hourly
and daily), seasonally (summer and winter), and from year to year (dry and wet years).
This variability in runoff could lead to variable generation, and problems in meeting
demand. The traditional solution to this is to build reservoirs and store water during
periods of surplus to be used in periods of drought.
0
The theoretical output of electrical power (P ) for a particular site depends on three
main factors, flow (Q), head (H), and efficiency in machinery (η) as illustrated here:

P ¼ ρ g Q H η (8.1)
0
0
Here P is the electrical power output (Js 1 ¼W); ρ is the density of water
2
3
(1000kgm ); g is the acceleration of gravity (9.81ms ); Q, the water flow per unit
3 1
time (m s ); H, the elevation drop, usually called head (m); η is the efficiency in the
conversion process from water to wire:
Potential energy ! kinetic energy ! mechanical energy ! electrical energy

Assuming typical values for density and acceleration of gravity as given here, the
equation can be simplified to give power output, P, directly in units of kilowatt:

P ¼ 9:81 Q H η (8.2)

The amount of energy produced depends on the duration of the flow. Assuming the Δt
is given in hours (h) the amount of energy, E (in units of kilowatt hours), produced can
be computed from:

(8.3)
E ¼ P Δt
For comparison to other renewable and thermal energy sources, the energy unit
Exajoule (where 1EJ ¼10 18 J) is often used. Here 1.0EJ¼277.78TWh and
1.0TWh¼0.0036EJ. The global hydropower production in 2016 was 4102TWh,
which is equivalent to 14.76EJ.
Another useful equation gives the energy output in kilowatt hours per cubic meter
of water as a function of H and η, and is often called the Energy equivalent of water
(EEKV), and is calculated as:

EEKV ¼ P 1h= Q 3600sÞ ¼ 9:81 H η=3600 (8.4)
ð
In addition to kilowatt hours (kWh), some other commonly used units of electrical
energy are megawatt hour (MWh), gigawatt hour (GWh), and terawatt hour (TWh):