Final answer:
To calculate the power that the pump must supply to the system, use the equation P = Q * ΔP, where P is power, Q is the flow rate, and ΔP is the pressure difference.
Step-by-step explanation:
The pressure difference can be found using the equation ΔP = ρ * g * Δh, where ρ is the density of the oil, g is the acceleration due to gravity, and Δh is the change in height between the reservoirs. Substitute the values into the equation P = Q * ΔP to find the power.
To calculate the power that the pump must supply to the system, we can use the equation P = Q * ΔP, where P is power, Q is the flow rate, and ΔP is the pressure difference. In this case, the flow rate is given as 0.20 m³/s. To find the pressure difference, we need to consider the change in height between the two reservoirs. Since the oil is being pumped from the lower reservoir to the upper reservoir, the pressure at the upper reservoir is higher than at the lower reservoir.
Using the equation ΔP = ρ * g * Δh, where ρ is the density of the oil, g is the acceleration due to gravity, and Δh is the change in height, we can find the pressure difference. Assuming the density of the oil is 900 kg/m³ and the height difference between the reservoirs is known, we can calculate ΔP.
Once we have ΔP and Q, we can substitute these values into the equation P = Q * ΔP to find the power that the pump must supply to the system.