Fluid mechanics - Conservation of mass problem

[theBEAST]

Homework Statement

Here is the question along with my attempt:

As you see in my second equation there are two unknowns, A_out and dm/dt.

I think my problem is that I don't exactly understand the equation. dm/dt is the net mass flow rate. For example if dm/dt is a positive number then there is more flowing into the nozzle than there is flowing out. In other words there is a build up of mass in the nozzle? I guess this isn't possible since we have a nozzle and that is why in this case dm/dt = 0? Because that is the only other way I can think of doing this problem but I am not too sure.

In what case could dm/dt be positive? I am guessing when there is a tank that can be filled... But how do I know that the nozzle doesn't have a small pouch where the mass can build on itself...?

Also when they say "mass flow rate through the nozzle" is this dm/dt or is it the mass flow INTO the inlet nozzle?

Thanks!

Edit: for those who read through my solution attempt, there is a mistake in the last line where I did my conversion from 80cm^2 to 80m^2. the 100cm/1m needs to be flipped.

 

[Simon Bridge]

dm/dt is usually the mass flow rate through the nozzle.

 

[Basic_Physics]

The equation of continuity states that the flow rate past one cross section of a pipe needs to be the same as that through another cross section

J = A₁v₁ = A₂v₂

This gives you the volume flow rate. If multiplied by the density of the liquid one would get the mass flow rate passing through a cross section of the pipe.