PHY.10:5.1 - Change speed to separate two drag accounts

A specimen moves through the same fluid at an imposed positive speed v. In the proposed operating range, account L takes the opposing force magnitude to be F=b v; account Q takes it to be F=c v². The coefficients are positive and constant under their respective accounts.

At v=1 m/s, an earlier calibrated force comparison places the true drag between 0.95 and 1.05 N. Thus L permits b between 0.95 and 1.05 N·s/m, while Q permits c between 0.95 and 1.05 N·s²/m². Both explain that observation.

A repeat at the same speed leaves this disagreement intact. Instead impose v=2 m/s while retaining specimen geometry and the fluid conditions on which the coefficients depend. L predicts a force between 1.9 and 2.1 N; Q predicts between 3.8 and 4.2 N. With an additional bounded force-readout error of ±0.1 N, the possible indications lie in [1.8,2.2] N and [3.7,4.3] N. They are disjoint.

The drive and readout must sustain that comparison. Under Q the required mechanical power can reach 8.4 W, since P=Fv. A 5 W drive cannot establish the proposed steady speed for every admitted Q response. A 10 W drive at that speed can meet this particular power demand, while its other operating limits remain relevant.

Suppose the comparison returns 2.05 N. It is compatible with L and incompatible with Q under the stated ranges and conditions. A return of 2.9 N instead disagrees with both. It prompts examination of the retained physical regime, parameter constraints and readout; it does not justify selecting whichever nominal curve is closer.

Heating or a geometry change can make a coefficient vary between runs. If that effect can span the separation, the test no longer has the same interpretation. Restore the shared condition, include the changed dependence or choose another contrast. Increasing speed without this return can defeat the very accounts being compared.