PH 623
EXERCISE 1 MAY 2024
WIND ENERGY PORTION
1. (a)
(b)
(c)
2. (a)
(b)
3.
Define the terms
(i) cut in wind speed,
(ii) cut out wind speed, and
(iii) rated wind speed of a wind turbine. A sketch may be very useful.
Differentiate between the terms (i) available and (ii) extractable wind power density of
a wind energy conversion system (WECS).
Write the mathematical expressions for the two laws that are used to extrapolate wind
speed vertically. State clearly the meaning of each symbol used.
Mention at least five parts of a wind turbine and give a brief description of the function
of each part.
From the basic principle that wind is air in motion, show that the power contained in
wind =½AV3 where  is the density of air, A is the area of the rotor and V is free
stream velocity of the wind.
(a) Differentiate between the term solidity and tip speed ratio of a rotor.
(b) Discuss the reasons why rotors with low solidity are preferred when designing wind
turbines.
4.
(a) Develop an expression for the Belt’s limit of a Wind Energy Conversion System using
the momentum theory for an ideal wind turbine ‘ State clearly the meaning of all the
symbols used and any assumptions made in the derivation.
(b) What is the physical significance of Belt’s limit in harvesting wind energy from a
given wind speed?
5. (a) A wind turbine with cut-in velocity 4 m/s and cut-out velocity 25 m/s is installed at a
site with Weibull shape factor 2.4 and scale factor 9.8 m/s.
(b) For how many hours in a day, will the turbine generate power?
(c) Estimate the probability of wind velocity to exceed 35 m/s at this site.
6.
(a) What is the difference between;
(i) a horizontal wind turbine and a vertical wind turbine? Illustrate the merits and
demerits of each.
(ii) Offshore and onshore wind farms.
(b) What is the Capacity factor of a wind farm?