ir moving at 10.0 m/s in a steady wind encounters a windmill of diameter 2.30 m and having an efficiency of 26.5%. The energy generated by the windmill is used to pump water from a well 28.0 m deep into a tank 2.30 m above the ground. At what rate in liters per minute can water be pumped into the tank?
___________L/min
To calculate the rate at which water can be pumped into the tank, we first need to determine the power generated by the windmill. Power is the rate at which energy is generated or consumed and is calculated using the formula:
Power = Energy / Time
In this case, the windmill generates energy, and we know its efficiency. The energy generated is given by:
Energy generated = Efficiency * Energy available
The energy available is the kinetic energy of the wind hitting the windmill blades. The formula for kinetic energy is:
Kinetic energy = 0.5 * mass * velocity^2
Since we don't know the mass of the wind, we can ignore it for now and focus on the velocity and the diameter of the windmill.
The area of the windmill blades can be calculated using the formula:
Area = π * (diameter/2)^2
Next, we can determine the rate at which water is pumped into the tank using the power generated by the windmill. We know that the work done to lift the water is equal to the change in potential energy:
Work done = Mass of water * g * Height
where "g" is the acceleration due to gravity.
Finally, we can convert the work done into liters per minute by relating it to the power generated:
Rate of pumping water = Work done / (Time * density of water)
Now, let's plug in the numbers and calculate the answer.
Given:
Velocity of the wind (v) = 10.0 m/s
Windmill diameter (d) = 2.30 m
Windmill efficiency = 26.5%
Depth of the well (h) = 28.0 m
Height of the tank (H) = 2.30 m
Step 1: Calculate the area of the windmill blades:
Area = π * (2.30/2)^2 = 4.15 m^2
Step 2: Calculate the energy generated by the windmill:
Energy available = 0.5 * Area * density of air * velocity^2
Energy generated = Efficiency * Energy available
Step 3: Calculate the work done to lift the water:
Work done = Mass of water * g * Height
Step 4: Calculate the rate of pumping water:
Rate of pumping water = Work done / (Time * density of water)
Let's calculate the answer.