A 1.5 kilowatt electric motor on a water well pumps water from 10 meters below the surface. The density of the water is 1 kilogram per liter. How many liters of water does the motor pump in one hour?
3; 40
To find out how many liters of water the motor pumps in one hour, we need to determine the flow rate of the water.
The power of the motor is given as 1.5 kilowatts. Power is defined as the work done per unit time. In this case, the work done is pumping the water.
Using the equation:
Power = Work / Time
We can rearrange the equation to solve for work:
Work = Power × Time
In this case, the power is 1.5 kilowatts and we want to find the work done in one hour. Since 1 kilowatt-hour (kWh) is equal to 1000 watts × 3600 seconds (1 hour), we can convert the time to seconds:
Time = 1 hour × 3600 seconds/hour = 3600 seconds
Now we can calculate the work done by the motor:
Work = 1.5 kilowatts × 3600 seconds = 5400 kilojoules (kJs)
The work done is equivalent to the energy transferred to the water. We can use this energy to calculate the volume of water pumped by considering the potential energy change of the water.
The potential energy change can be expressed as:
Potential Energy Change = mass × gravity × height
In this case, the height is given as 10 meters below the surface. We can use the given density of water to convert the mass of water into volume:
Density of Water = 1 kilogram/liter
Now we can rearrange the equation to solve for the volume of water:
Volume = Potential Energy Change / (Density of Water × gravity)
where gravity is approximately 9.8 meters/second^2.
Volume = 5400 kJs / (1 kilogram/liter × 9.8 meters/second^2)
Volume = 5400 / (9.8) liters
So, the motor pumps approximately 551 liters of water in one hour.