Question

A 10 hp motor pumps out water from a well of depth 20 m and fills a water tank of volume 2238 liters at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is (g = 10m/s²)

• A. 5 minutes
• B. 10 minutes
• C. 15 minutes
• D. 20 minutes

Answer 1

1.5 minutes

Answer 2

1. Calculate work required:

   • Volume = 2238 liters = 2.238 m³
   • Mass of water m = ρ × Volume = 1000 × 2.238 = 2238 kg
   • Water is raised from the bottom of a 20 m deep well to a tank 10 m above ground so effective height h = 20 + 10 = 30 m
   • Required work (increase in potential energy) W = m g h = 2238 × 10 × 30 = 671400 J

2. Determine available power:

   • Motor rating = 10 hp, and 1 hp = 746 W, so P = 10 × 746 = 7460 W

3. Find time required:

   • Time t = W/P = 671400 / 7460 ≈ 90 sec = 1.5 minutes

The motor takes about 1.5 minutes to fill the tank.