Try this with a desk fan: turn it on and stand a meter away on the outflow side - you will feel the flow. Stand a meter away on the inflow side, and the flow is

Try this with a desk fan: turn it on and stand a meter away on the outflow side - you will feel the flow. Stand a meter away on the inflow side, and the flow is much weaker and probably undetectable. That's because it is flowing in over a whole hemisphere upstream of the fan, but flowing out in essentially one direction. Here, as with the anemometer, you are not measuring the total mass flow; what's being measured is the velocity of part of that flow, and you are intercepting more of that flow on the outflow side. If you were to measure and integrate the velocity over two hemispheres centered on the fan and divided by the plane of the blades, with a barrier in that plane to prevent recirculation, and calculate the mass flow from that (you can assume constant density as the pressure change is tiny), you will find that the total outflow downstream equals the total inflow upstream.† † To actually do this experiment, you will need a sensitive anemometer which measures over a small area and does not unduly interfere with the flow, such as a hot-wire probe type. There may be additional difficulties in averaging turbulence. https://electricalworkbook.com/hot-wire-anemometer/ https://electricalworkbook.com/hot-wire-anemometer/