Air moving at 13.0 m/s in a steady wind encounters a windmill of diameter 2.30 m and having an efficiency of 29.0%. The energy generated by the windmill is used to pump water from a well 31.0 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?

To find the rate at which water can be pumped into the tank, we need to determine the power generated by the windmill.

First, let's calculate the area of the windmill's blades:

Area = π * (radius^2)

Radius = diameter / 2 = 2.30 m / 2 = 1.15 m

Area = π * (1.15 m)^2

Next, we'll determine the kinetic energy of the moving air:

Kinetic Energy = (1/2) * mass * velocity^2

The mass of the air can be calculated using the equation:

Mass = density * volume

Assuming the air is at standard conditions (density = 1.225 kg/m^3), we can calculate the volume of air passing through the windmill per unit time:

Volume = Area * velocity

Using the equation P = ∆E / ∆t, where P is the power, and ∆E / ∆t is the change in energy over time.

Next, we'll calculate the power generated by the windmill:

Power = Efficiency * Kinetic Energy

Finally, we'll convert the power to liters per minute by relating it to the mass of water lifted:

1 liter of water = 1 kg

So, the rate at which water can be pumped into the tank can be found by dividing the power by the weight of the water (∆m/∆t) using the equation:

Rate = Power / (∆m/∆t)

Now, let's calculate the rate at which water can be pumped into the tank.