Write a function, determine_windpower(v_hub, r, rho), which determines the wind power inkW, given the wind speed at the hub, v_hub ( m/s), the radius of the blades, r ( m ), and the airdensity rho (kg/m3). To do the calculation you can use the relation:Pwind = 12 ρA (vhub)3 = 12 ρπr 2 (vhub)3 (2)A sample usage of the function is given below
Question
Write a function, determine_windpower(v_hub, r, rho), which determines the wind power inkW, given the wind speed at the hub, v_hub ( m/s), the radius of the blades, r ( m ), and the airdensity rho (kg/m3). To do the calculation you can use the relation:Pwind = 12 ρA (vhub)3 = 12 ρπr 2 (vhub)3 (2)A sample usage of the function is given below
Solution
Here is a Python function that implements the formula you provided:
import math
def determine_windpower(v_hub, r, rho):
# Calculate the area of the blades
A = math.pi * r**2
# Calculate the wind power
P_wind = 0.5 * rho * A * v_hub**3
# Convert the wind power from watts to kilowatts
P_wind = P_wind / 1000
return P_wind
You can use this function like this:
# Define the wind speed at the hub, the radius of the blades, and the air density
v_hub = 10 # m/s
r = 5 # m
rho = 1.225 # kg/m^3
# Determine the wind power
P_wind = determine_windpower(v_hub, r, rho)
# Print the wind power
print(f"The wind power is {P_wind} kW.")
This will calculate the wind power based on the given wind speed at the hub, the radius of the blades, and the air density. The wind power is calculated using the formula you provided, and then it is converted from watts to kilowatts.
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