So, you are changing the voltage, which changes the slip, which slightly changes the speed, and without changing the system, you are observing changes in flow rate and input electric power, correct?
Some things to consider:
1 - The pump/fan laws DON'T tell us what happens to the operating point with change in sped. They tell us what happens to the pump curve. To convert that knowledge of change in pump curve to knowledge of change in operating point, we would need to know sometihng about the SYSTEM characteristic curves (the operating point is the intersection). As it turns out, ONLY if the system characteristic curve obeys DP~flow^2 do these relations apply directly to the operating point.
2 - affinity laws apply to incompressible fluid. For a fan, they are pretty close if the dp is far less than the absolute pressure (so that pressure and density don't change by a large factor). They are not good if the dp is a sizeable fraction of the absolute pressure, such that density is not even close to constant.
3 - affinity laws apply to bhp, but you are measuring input power I think. If there is significant change in efficiency then you have an error.