Fluid flow through a pipe - Conservation of mass and/or momentum?

[theBEAST]

Homework Statement

The Attempt at a Solution

So first I found the density of the air coming in and going out. Next I used conservation of momentum with two forces caused by the pressures at the entrance and the exit of the nozzle.

I end up getting 1004 which is not the same as 1060. If I just use conservation of mass so ρVA_out=ρVA_in I get exactly 1060. So why is it that conservation of momentum does not work in this scenario?

 

[SteamKing]

The nozzle is accelerating the flow of the fluid through the restriction. The mass flow into the nozzle is the same as the mass flow out, but the velocity has increased while the density decreases.