A water pump produces 9kl of water per hour at height of 70m above the pump. The pump is driven by 3kW electric motor calculate

1.the work done per hour.
2.the work done per minute.

A kL is 1 meter^3

density of water is 1000 kg/m^3
potential energy gained in one hour = m g h = 9 *1000 *9.81 * 70
= 6,180,300 Joules / hr
divide by 60 to get Joules /minute = 103,005 Joules/minute
by the way
divide by 60 again to get Joules per second or watts
= 1717 watts =1.7 kW
so the motor / pump system is around 50% efficient

1. m * g * h ... 9000 kg * 9.8 m/s^2 * 70 m Joules

2. divide #1 by 60

To solve this problem, we need to use the formula for work done:

Work (W) = power (P) × time (t)

Given information:
Power (P) = 3 kW
Time (t) = 1 hour

1. To calculate the work done per hour:

Work (W) = Power (P) × Time (t)
Work = 3 kW × 1 hour

To convert kilowatts to watts, we use the conversion: 1 kilowatt (kW) = 1000 watts (W).

Work = 3,000 W × 1 hour
Work = 3,000 W × 3,600 seconds (since there are 3600 seconds in an hour)

Therefore, the work done per hour is 10,800,000 joules.

2. To calculate the work done per minute:

We know that work done per hour is 10,800,000 joules.

To convert the work done per hour to work done per minute, we divide by 60 (since there are 60 minutes in an hour).

Work per minute = Work per hour ÷ 60
Work per minute = 10,800,000 joules ÷ 60

Therefore, the work done per minute is 180,000 joules.

To calculate the work done per hour by the water pump, we need to determine the amount of energy required to pump the water up to the height of 70m.

1. Work done per hour:
The work done by the water pump can be calculated using the following formula:
Work = Force × Distance

First, let's calculate the force required to lift the water. We know that the weight of water is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2):
Weight of water = Volume of water × Density of water × Acceleration due to gravity

Given that the pump produces 9 kl (kiloliters) of water per hour, which is equivalent to 9000 liters of water:
Volume of water = 9000 L

The density of water is approximately 1000 kg/m^3.

Now we can calculate the weight of water:
Weight of water = 9000 L × 1000 kg/m^3 × 9.8 m/s^2

Next, we need to convert the weight to force since force is equal to mass multiplied by acceleration:
Force = Weight of water × gravitational acceleration

Now we can calculate the force:
Force = (9000 L × 1000 kg/m^3 × 9.8 m/s^2) × 1 N/kg

Finally, we can calculate the work done in one hour by multiplying the force by the distance:
Work = Force × Distance

Given that the height is 70m and the pump produces 9kl of water per hour:
Work done per hour = Force × Distance = (9000 L × 1000 kg/m^3 × 9.8 m/s^2) × 1 N/kg × 70 m

Now, let's calculate the work done per hour:

Work done per hour = (Force × Distance) × 3600 seconds/hour

2. Work done per minute:
To calculate the work done per minute, we divide the work done per hour by 60 (since there are 60 minutes in an hour):

Work done per minute = Work done per hour / 60

Now you can substitute the given values into the formulas and calculate both the work done per hour and the work done per minute.