A pond will be built to store water to irrigate vegetables. The volume of the pond and the time to fill the pond need to be determined.

Assumptions:

• No irrigation during the filling process
• The flow of the pump is steady, m = t (Steady flow process will be introduced in the following sections)

(1) Determine the volume of the pond

The amount of water needed for 45 acres per day:

      V_total = (45)(2,000) = 90,000 L

At the end of the filling process, the pond should have enough water to irrigate the 45 acres for the day. Hence the volume of the pond needs to be at least 90,000 L.

(2) Determine the filling time

Considering the water in the pond as a system. During the filling process, no water is going out of the system for irrigation. The mass balance on this system during the filling process is:

At the end of the filling process, the pond has the water needed for one day's irrigation. That gives

      m_system@final = m_total

At the beginning of the filling process, the pond is empty.

      m_{system@initial} = 0

From the mass balance, the mass imported to the pond can be determined.

      m_in = Δm_system = m_system@final - m_{system@initial}
                    = m_total - 0
                    = V_totalρ
                    = (90,000/1,000)(996)
                    = 89,640 kg

      m_in= 89,640 kg

The flow rate of the pump is 20 L/s, or = 20 L/s. According to the relation between the mass flow rate and volume flow rate, the mass flow rate can be determined.

       = ρ = (20/1,000)(996) = 19.9 kg/s

The total time needed for the pump to be operated is:

      m_in = t

      t = m_in/ = (89,640)/(19.9) = 4505 s = 1.25 h