Determine the instantaneous power for the wind turbine with

Question

Assignment -

Problem: Derive the Betz constant using the Coefficient of Performance equation. Similarly, derive the maximum value for the Coefficient of Thrust.

Problem: During a typical day, a weather station records the following data for a 60-min period.

Minute	mph	Minute	mph	Minute	mph	Minute	mph
1	14.6	16	11.8	31	13	46	11.3
2	13.9	17	10.6	32	11.9	47	12
3	13.9	18	12.5	33	13.3	48	11.2
4	13.5	19	10.9	34	12.9	49	10.9
5	13.4	20	11.7	35	13.6	50	10.3
6	14.2	21	11.7	36	13.3	51	9.7
7	13.1	22	12.3	37	12	52	9.8
8	12.5	23	11	38	11.6	53	8.9
9	11.9	24	13.2	39	12.1	54	8.5
10	11.5	25	12.5	40	12.2	55	9.1
11	11.7	26	11.7	41	11.8	56	9.9
12	10.7	27	11.2	42	12.5	57	11.1
13	11.9	28	12.6	43	11.6	58	11
14	11.9	29	12.6	44	12.5	59	10.7
15	11.8	30	12.5	45	11.6	60	9.6

In addition, the following data is available:

• The air density (r) is 1.18 kg/m³.
• The wind turbine has a diameter of 3.2 m.
• Coefficient of performance C_p = 0.2, aerodynamic efficiency h_p = 0.92, mechanical efficiency h_t = 0.95 and generator efficiency is h_g = 0.90.

Determine:

a) Instantaneous power for the wind turbine with three rotors as a function of time for a 60-minute period.

b) Energy produced in kW-hr (use calculated power to derive this) for the 60- minute period and use that to calculate daily, weekly, monthly and annual energy collected.

c) Assuming the system operated at its Betz limit, repeat (a), (b) and (c).

d) Assuming you only needed to produce the annual energy in (b) and the wind turbine is operating at its Betz limit, discuss what changes you will adopt in your wind turbine design.

e) Is the location for which the wind conditions are provided in the table better suited than Carlsbad, CA. Provide a technical explanation for your answer.

Need clear and accurate answer.