Water enters a 4.00-m3 tank at a rate of 6.33 kg/s and is withdrawn at a rate of 3.25 kg/s. the tank is initially half full.
how long does it take for the tank to overflow?

Explanation:

The given data is as follows.

            Volume of tank = 4

             Density of water = 1000

Since, the tank is initially half-filled. Hence, the volume of water in the tank is calculated as follows.

Also, density of a substance is equal to its mass divided by its volume. Therefore, initially mass of water in the tank is as follows.

                    Mass =

                              =

                              = 2000 kg

Whereas mass of water in tank when it is full is as follows.

                     Mass =

                               =

                               = 4000 kg

So, net mass of the fluid to be filled is as follows.

                  Net mass to be filled = Final mass - initial mass

                                                      = 4000 kg - 2000 kg

                                                      = 2000 kg

Mass flow rate = 6.33 kg/s

Mass flow rate = 3.25 kg/s

       Time needed to fill tank =

                                       =

                                       =

                                       = 649.35 sec

Thus, we can conclude that 649.35 sec is taken by the tank to overflow.