Question

At an orange juice plant, orange juice pulp with a density of 1.25 g/ml passes through a pumping station where it is raised vertically by 5.76 m at the rate of 1,920,000 liters per day. The liquid enters and leaves the pumping station at the same speed and through pipes of equal diameter. (a) Determine the output mechanical power (in W) of the lift station. Ignore any energy loss due to friction. (b) Assume an electric motor continuously operating with average power 3.70 kW runs the pump. Find its efficiency.

Answer 1

To calculate the output mechanical power of the lift station, use the formula: Power = Density * g * Volume Flow Rate * Height. To find the efficiency of the electric motor, use the formula: Efficiency = (Output Power / Input Power) * 100%.

Step-by-step explanation:

To calculate the output mechanical power of the lift station, we can use the formula: Power = Density * g * Volume Flow Rate * Height. We are given that the density of the orange juice pulp is 1.25 g/ml, the volume flow rate is 1,920,000 liters per day, and the height is 5.76 m. First, we need to convert the volume flow rate to cubic meters per second by dividing it by 86400 (the number of seconds in a day). Then, we convert the density to kg/m³ by multiplying it by 1000. Finally, we plug the values into the formula to calculate the output mechanical power.

(b) The efficiency of an electric motor can be calculated using the formula: Efficiency = (Output Power / Input Power) * 100%. We are given that the motor has an average power of 3.70 kW. To find the input power, we need to convert the volume flow rate from liters per day to cubic meters per second, and then calculate the input power using the formula: Input Power = Density * g * Volume Flow Rate * Height. Once we have the input and output power, we can calculate the efficiency using the given formula.