Question

A Sprinkler consisting of an open square tank 60 cm on a side discharges 1.0 kg/s of water through holes in the tank bottom. If the tank is half full at a at a certain time, how great a flow must be provided from an external faucet to fill the tank to top with water in 2 min if the discharge is constant at 1.0 kg/s

Answer 1

To solve this problem we will apply the concepts related to the mass flow which is described as the amount of mass per unit of time. To get there we must find the mass from the volume so we will use the density ratio. Volume is

`\text{Volume} = V = (0.6)(0.6)(0.6) = 0.216m^3`

The half tank is full then,

`\text{Empty Volume} = (0.216m^3)/(2) = 0.108m^3`

The density ratio tells us that it is equal to the change in mass per volume so

`\rho = (m)/(V) \Rightarrow m = \rho V`

Replacing with our values,

`m = (1000kg/m^3)(0.108m^3)`

`m = 108kg`

The rate of change of the mass is equivalent to the mass per unit time then

`\dot{m} = \frac{\text{Mass}}{\text{Time}}`

`\dot{m} = (108)/(2*60)`

`\dot{m} = 1.8kg/s`

But there is an initial discharge of 1kg / s so the net flow would be

`\dot{m}_(Net) = \dot{m}'+\dot{m}`

`\dot{m}_(Net) = 1+1.8`

`\dot{m}_(Net) = 2.8kg/s`

Therefore 2.8kg/s mass should be entered to fill the tank in 2 min