Hydro/Wind Power Generation Flashcards
How does hydro/tidal power generation work?
A dam or a barrage blocks flow of water. Water is taken from the top of the dam through pipes which gains kinetic energy.
What is the equation for kinetic and gravitational potential energy?
KE = 1/2 mv^2 GPE = mgh
How do we find the velocity of the falling water?
Set KE = GPE and rearrange for v.
What is the equation for the power output of a hydro power generator?
P = ρ(water)ghQ, where Q is the flow rate (volume per second), or vA, where A is the cross sectional area of the turbine entry
How can hydro stations be used to store energy?
- Capacity defined by mass of reservoir and the drop
- Can pump water back up drop using unneeded energy - allows for power supply on demand.
What percentage does hydro power account for in the world?
16%
What is tidal power?
Gravitational force to the Moon and centrifugal force of the rotation Earth-Moon system produce two bulges of water.
How can we use the tide to generate electricity?
Let tide get in estuary, close gate until tide goes out and then open gate, making water flow through turbine,
What is the total potential energy of tidal water stored in estuary?
Sgρ(water)*R^2/2T, where S is the area of the basin, and T is the tide period (~12 hours)
What is a pro of hydro power?
Easy to control flow of water and integrate with the grid.
What is a con of hydro power?
Most sites in the UK are developed - difficult to create large reservoirs of water.
What is a pro of tidal power?
Possible to extract energy from underwater turbines driven by tidal currents.
What is a con of tidal
power?
Harder to integrate to grid as power rate is time dependent.
For wind at speed v going through turbine of area A, what is the mass, KE and therefore power of the wind going through the turbine?
- Mass = ρ(air)Av*Δt
- KE = ρ(air)Av^3*Δt/2
- Power = ρ(air)Av^3/2
What does Betz law show?
The limitations of wind turbines (they absorb some power, so aren’t 100% efficient).
What is the first step in deriving Betz law?
- A1, v1 on left and A2, v2 on right after going through turbine
- Set KE equations on left and right equal to each other accordingly (including turbine area and velocity, A,v)
What is the power absorbed by the turbine equal to?
KE on left - KE on right, so rearranged is: ΔP = 1/2 * ρ(air)Av(v1^2 - v2^2) = Fv
What is the velocity of the air passing through the turbine equal to?
v = 1/2 * (v1+v2)
What is the final equation for the power of the turbine?
P = 1/2 * ρ(air)AV1^3 * Cp
What is the approximate cut-in and cut-out velocities for large modern turbines?
Cut-in ~ 4 ms^-1
Cut-out ~ 25 ms^-1
What is the rated power?
Velocity of wind at which power output is flat until the cut-out velocity.
If we have a fluctuating wind with v(t), what is the equation for the average value of v^3?
1/T * integral from 0 to T of (V(t))^3 dt >= (V(average))^3
What is the typical value for v(rate)?
~12 ms^-1
What is the equation for the averaged power <p>?</p>
integral from 0 to inf of P(v)*f(v) dV = c(f) * P(rate), where f(v) is the wind speed distribution
What is the approximate distance turbines can be put next to eachother?
~10a, where a is the turbine blade length
What is the power per surface area σ equal to for a wind turbine?
<p>/(100*a^2) = π*ρ(air)/200 * c(f) * c(p) * (v(rate)^3, where c(f) if the capacity factor determined by the site.</p>
What is an interesting conclusion from the power per surface area?
It does not depend on the length of the turbine blades.
Where is the best place to build wind turbines?
Offshore as the wind is stronger and there is lots of free space.
