#1.) A wind turbine has a Cp of 0.42 and extracts 50 kW of power when the wind velocity is 25 m/sec. How long are the blades? (ρ = 1.2 kg/m3)
#2.) An electric hot water heater is used to heat 30 gallons of water from 20 °C to 45 °C.
a. What heat energy is required to increase its temperature?
b. What electric energy (still in Joules) is required if the efficiency is 98%?
c. If this heat energy flows into the water a constant rate over a 30 minute period, what power is
required over this period?
d. If this power is delivered by a resistive hot water heating element using a 240 V source, what must the resistance of the heating element be?
heattoheatwater=masswater*specific*(45-20)
figure mass water from volume and denstity, look up specific heat.
if eff is .98, then energy=heat/.98
power=heateneryg/timeinseconds
R=V^2/energy
To solve problem #1, we can use the power equation for a wind turbine.
The power captured by a wind turbine can be calculated using the equation:
P = 0.5 * Cp * ρ * A * V^3
Where:
P is the power captured by the wind turbine
Cp is the power coefficient (provided as 0.42)
ρ is the air density (provided as 1.2 kg/m^3)
A is the swept area of the rotor blades
V is the wind velocity
We know that the power captured by the wind turbine is 50 kW (kilowatts) and the wind velocity is 25 m/s (meters per second). We can substitute these values into the equation and solve for A, the swept area of the rotor blades.
50,000 = 0.5 * 0.42 * 1.2 * A * (25^3)
Now, rearranging the equation to solve for A:
A = (50,000 / (0.5 * 0.42 * 1.2 * (25^3)))
Calculating the value of A:
A ≈ 330.61 m^2
The swept area of the rotor blades is approximately 330.61 square meters.
To find the length of the blades, we need to know the shape of the rotor blades (e.g., rectangular, triangular, etc.). Without this information, it is not possible to directly calculate the length of the blades. This problem requires additional information to solve accurately.