Respuesta :
Explanation:
The given data is as follows.
Volume of tank = 4 [tex]m^{3}[/tex]
Density of water = 1000 [tex]kg/m^{3}[/tex]
Since, the tank is initially half-filled. Hence, the volume of water in the tank is calculated as follows.
[tex]\frac{1}{2} \times 4 = 2 m^{3}[/tex]
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 = [tex]Density \times initial volume[/tex]
= [tex]1000 \times 2[/tex]
= 2000 kg
Whereas mass of water in tank when it is full is as follows.
Mass = [tex]Density \times final volume[/tex]
= [tex]1000 \times 4[/tex]
= 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 [tex](m_{in})[/tex] = 6.33 kg/s
Mass flow rate [tex](m_{out})[/tex] = 3.25 kg/s
Time needed to fill tank = [tex]\frac{\text{net mass to be filled}}{\text{net difference of flow rates}}[/tex]
= [tex]\frac{2000 kg}{m_{in} - m_{out}}[/tex]
= [tex]\frac{2000 kg}{6.33 kg/s - 3.25 kg/s}[/tex]
= 649.35 sec
Thus, we can conclude that 649.35 sec is taken by the tank to overflow.
