Question

At a bottled water plant, water with a density of 1.00 g/ml passes through a pumping station where it is raised vertically by 5.72 m at the rate of 1,880,000 liters per day. The liquid enters and leaves the pumping station at the same speed and through pipes of equal diameter. Determine the output mechanical power (in W) of the lift station. Ignore any energy loss due to friction.

Answer 1

The output mechanical power of the lift station at a bottled water plant, elevating water at a rate of 1,880,000 liters per day through a height of 5.72 meters, is 1,216.3 watts.

Step-by-step explanation:

To determine the output mechanical power of the lift station at a bottled water plant, we can use the formula for power = work/time, where work = force × distance. Since the question provides the rate of water flow and the height to which it is being lifted, we can use the density of water to convert the volume flow rate to mass flow rate and then calculate the work done to lift the water.

First, we convert the daily volume flow rate to a mass flow rate:
1,880,000 liters/day × 1,000 g/L = 1,880,000,000 g/day or 1,880,000 kg/day
Next, we convert this to a per-second rate since power is in watts (joules/second):
1,880,000 kg/day / (24 × 60 × 60 seconds) = 21.759 kg/s
Now, we calculate the work done (ΔPE = mgh):
21.759 kg/s × 9.8 m/s² × 5.72 m = 1,216.3 J/s or W
Thus, the pump's output mechanical power is 1,216.3 watts.