What factors need to be considered to determine the number of liters of water pumped by a 2.0 hp electric motor in 1 hour?
The electric motor with a power of 2.0 hp pumps water from a depth of 10 m below the surface. To determine the number of liters of water pumped in 1 hour, we need to consider the power of the motor and the density of water.
Calculating the Volume of Water Pumped
Power Conversion:
First, let's convert the power from horsepower (hp) to watts (W). 1 hp is approximately equal to 745.7 W. Therefore, the power of the motor is:
P = 2.0 hp * 745.7 W/hp = 1491.4 W
Volume Calculation:
Next, we use the formula to calculate the volume of water pumped per second (Q):
Q = P / (ρ * g * h)
Where:
P is the power in watts (1491.4 W),
ρ is the density of water (1.0 kg/L or 1000 kg/m³),
g is the acceleration due to gravity (approximately 9.8 m/s²),
h is the height or depth the water is lifted (10 m).
Substituting the values into the formula:
Q = 1491.4 W / (1000 kg/m³ * 9.8 m/s² * 10 m)
Q ≈ 0.152 m³/s
Conversion to Liters:
Since there are 1000 liters in 1 cubic meter, we convert the volume from cubic meters to liters:
Q = 0.152 m³/s * 1000 L/m³ = 152 L/s
Volume Pumped in 1 Hour:
To find the volume of water pumped in 1 hour, we multiply the flow rate by the number of seconds in an hour:
Volume pumped in 1 hour = 152 L/s * 3600 s = 547,200 L
Therefore, the electric motor pumps approximately 547,200 liters of water in 1 hour.