Answer :
Final answer:
The power required to pump water from a borehole that is 15.0 m deep at a rate of 20.0 liters per second is calculated using the equation P = ρghQ. With the given values for the density of water, gravitational acceleration, height, and flow rate, the power is found to be 2943 Watts.
Explanation:
To calculate the power required to pump water from a borehole of depth 15.0 m at a rate of 20.0 liters per second, we need to use the concept of the power equation in fluid mechanics, which combines flow rate, gravitational acceleration, fluid density, and height difference.
The general power equation is given by P = ρghQ, where ρ (rho) is the density of the fluid, g is the acceleration due to gravity, h is the height the water is being lifted, and Q is the volumetric flow rate.
Using the provided values: ρ (density of water) = 1000 kg/m³, g = 9.81 m/s², h = 15.0 m, and Q = 20 liters/s which is equal to 0.020 m³/s, we can calculate the required power.
P = 1000 kg/m³ × 9.81 m/s² × 15.0 m × 0.020 m³/s
P = 2943 Watts
Therefore, the power required to pump the water from the borehole under the given conditions is 2943 Watts.
