Hydro/Wind Power Generation

Question 1

How does hydro/tidal power generation work?

Answer 1

A dam or a barrage blocks flow of water. Water is taken from the top of the dam through pipes which gains kinetic energy.

Question 2

What is the equation for kinetic and gravitational potential energy?

Answer 2

KE = 1/2 mv^2
GPE = mgh

Question 3

How do we find the velocity of the falling water?

Answer 3

Set KE = GPE and rearrange for v.

Question 4

What is the equation for the power output of a hydro power generator?

Answer 4

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

Question 5

How can hydro stations be used to store energy?

Answer 5

• Capacity defined by mass of reservoir and the drop

- Can pump water back up drop using unneeded energy - allows for power supply on demand.

Question 6

What percentage does hydro power account for in the world?

Answer 6

16%

Question 7

What is tidal power?

Answer 7

Gravitational force to the Moon and centrifugal force of the rotation Earth-Moon system produce two bulges of water.

Question 8

How can we use the tide to generate electricity?

Answer 8

Let tide get in estuary, close gate until tide goes out and then open gate, making water flow through turbine,

Question 9

What is the total potential energy of tidal water stored in estuary?

Answer 9

Sgρ(water)*R^2/2T, where S is the area of the basin, and T is the tide period (~12 hours)

Question 10

What is a pro of hydro power?

Answer 10

Easy to control flow of water and integrate with the grid.

Question 11

What is a con of hydro power?

Answer 11

Most sites in the UK are developed - difficult to create large reservoirs of water.

Question 12

What is a pro of tidal power?

Answer 12

Possible to extract energy from underwater turbines driven by tidal currents.

Question 13

What is a con of tidal

power?

Answer 13

Harder to integrate to grid as power rate is time dependent.

Question 14

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?

Answer 14

• Mass = ρ(air)Av*Δt
• KE = ρ(air)Av^3*Δt/2
• Power = ρ(air)Av^3/2

Question 15

What does Betz law show?

Answer 15

The limitations of wind turbines (they absorb some power, so aren’t 100% efficient).

Question 16

What is the first step in deriving Betz law?

Answer 16

• 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)

Question 17

What is the power absorbed by the turbine equal to?

Answer 17

KE on left - KE on right, so rearranged is: ΔP = 1/2 * ρ(air)Av(v1^2 - v2^2) = Fv

Question 18

What is the velocity of the air passing through the turbine equal to?

Answer 18

v = 1/2 * (v1+v2)

Question 19

What is the final equation for the power of the turbine?

Answer 19

P = 1/2 * ρ(air)AV1^3 * Cp

Question 20

What is the approximate cut-in and cut-out velocities for large modern turbines?

Answer 20

Cut-in ~ 4 ms^-1

Cut-out ~ 25 ms^-1

Question 21

What is the rated power?

Answer 21

Velocity of wind at which power output is flat until the cut-out velocity.

Question 22

If we have a fluctuating wind with v(t), what is the equation for the average value of v^3?

Answer 22

1/T * integral from 0 to T of (V(t))^3 dt >= (V(average))^3

Question 23

What is the typical value for v(rate)?

Answer 23

~12 ms^-1

Question 24

What is the equation for the averaged power <p>?</p>

Answer 24

integral from 0 to inf of P(v)*f(v) dV = c(f) * P(rate), where f(v) is the wind speed distribution

Question 25

What is the approximate distance turbines can be put next to eachother?

Answer 25

~10a, where a is the turbine blade length

Question 26

What is the power per surface area σ equal to for a wind turbine?

Answer 26

<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>

Question 27

What is an interesting conclusion from the power per surface area?

Answer 27

It does not depend on the length of the turbine blades.

Question 28

Where is the best place to build wind turbines?

Answer 28

Offshore as the wind is stronger and there is lots of free space.