To calculate the horsepower needed for a pump to raise water from a depth of 50 meters at a flow rate of 2 kg/s and an ejection speed of 10 m/s, one must consider both the potential energy required to lift the water and the kinetic energy needed to accelerate it. The potential energy can be calculated using the formula E_p = mgh, resulting in 981 J/s for lifting, while the kinetic energy is calculated using E_k = 1/2 mv^2, yielding 100 J/s for acceleration. The total energy required per second is the sum of these energies, which is 1081 J/s. To convert this to horsepower, divide by 745.7, resulting in approximately 1.45 horsepower. Understanding the distinction between lifting and accelerating the water is crucial for accurate calculations.
