The power required to drive a pump is calculated by considering:

Explanation:

In the context of pump operation, the power required to drive a pump is a critical factor that needs to be calculated accurately to ensure efficient and effective performance. The correct option in this scenario is option 3: "the work done in overcoming hydraulic losses and delivering the desired head." This is because the primary purpose of a pump is to move fluid from one place to another, and this process involves overcoming various hydraulic resistances and achieving the necessary head (height) to which the fluid must be raised.

Detailed Explanation:

The power required to drive a pump is determined by the following key factors:

1. Hydraulic Power Output: This is the power required to achieve the desired flow rate and head. It can be calculated using the formula:

Hydraulic Power (P_h) = (Q × H × ρ × g) / η

where:

• Q = Flow rate of the fluid (m³/s)
• H = Head (height) to which the fluid is pumped (m)
• ρ = Density of the fluid (kg/m³)
• g = Acceleration due to gravity (9.81 m/s²)
• η = Efficiency of the pump (decimal form, e.g., 0.8 for 80% efficiency)

2. Hydraulic Losses: These include losses due to friction within the pump, losses in the piping system, and losses due to turbulence. These losses must be overcome by the pump to maintain the desired flow rate and head.

3. Mechanical Power Input: This is the actual power input required from the motor or engine driving the pump. It can be calculated by dividing the hydraulic power by the efficiency of the pump:

Mechanical Power (P_m) = P_h / η

where:

• P_h = Hydraulic Power (W)
• η = Efficiency of the pump (decimal form)

By considering both the hydraulic power output and the hydraulic losses, we can accurately determine the power required to drive the pump. This ensures that the pump operates efficiently and effectively, delivering the desired flow rate and head with minimal energy wastage.