Power Calculation: Sump Pump Moving 20 gal/min

[Boyko]

Homework Statement

A sump pump moves 20 gal/min of water from a basement of a building to storm drain 6ft above. Determine the power required for the pump. (Assume the pump is 100% efficient and that changes in kinetic energy are negligible.)

Homework Equations

Power= Work x Time
Kinetic Energy=1/2mV^2

The Attempt at a Solution

The equation can be re-written as Power= Force x Velocity but I am unsure of how to continue with this problem. Any help getting me on the right track would be very appreciated.

 

[nilesh_pat]

Since the pump is 100% efficient, the power required will be equal to the work done by the pump. The work done by the pump will be the energy to lift the water 6 feet.The equation for work done is W=F*d, where F is the force and d is the distance. Since the mass of the water is known (20 gal/min = 20 gal/60 sec = 1/3 gal/sec), the force can be determined using the equation F=ma, where m is the mass and a is the acceleration due to gravity, which is 9.8m/s^2.Therefore, F= (1/3 gal/sec)*(9.8m/s^2) = 3.27NThe power required for the pump will be the work done times the time:Power = W * t = (F * d) * t = (3.27N * 6ft) * (1min/60sec) = 0.546 Watts

 

[piercas]

I would approach this problem by first making some assumptions and clarifications. Since the problem states that the pump is 100% efficient and changes in kinetic energy are negligible, we can assume that all of the power required for the pump is used to overcome the force of gravity to move the water from the basement to the storm drain. Additionally, we can assume that the water being pumped is at rest at both the starting and ending points, so there is no change in kinetic energy.

With these assumptions in mind, we can apply the equation for work (W = Fd) to calculate the force required to move the water. The distance (d) in this case is the height difference between the basement and the storm drain (6ft or 1.83m). The force (F) is equal to the weight of the water being pumped, which can be calculated using the density of water (1000 kg/m^3) and the volume being pumped per minute (20 gal/min or 0.0757 m^3/min).

F = (density)(volume/time) = (1000 kg/m^3)(0.0757 m^3/min) = 75.7 kg/min

To convert this force to Newtons (N), we can use the conversion factor 1 kg = 9.8 N.

F = (75.7 kg/min)(9.8 N/kg) = 742.86 N/min

Now that we have the force required, we can calculate the power using the equation Power = Force x Velocity. The velocity (V) in this case is the speed at which the water is being pumped (20 gal/min or 0.0757 m^3/min).

Power = (Force)(Velocity) = (742.86 N/min)(0.0757 m^3/min) = 56.24 Watts

Therefore, the power required for the sump pump to move 20 gal/min of water from a basement to a storm drain 6ft above is approximately 56.24 Watts. This information can be useful in selecting an appropriate pump for the job and ensuring that enough power is available to effectively move the water.