Calibrating distance in an endless pool

Does anyone have any idea what any potential correlation there is between power setting on an endless pool and current speed?

They say that at full speed, the endless pool provides enough counter current to do 1 mile in about 20 minutes. Well, thats great - but the power setting on the pool is in the units of pressure, and I dont know that it scales linearly throughout the range. In other words, if the max setting (pressure) is 110 bar (or whatever the unit is), and that does a ‘speed’ of 3 mph - does half that setting of 55 equate to 1.5 mph?

I don’t think it’s linear. Bernoulli tells us that in a closed system, pressure is going to be proportional to half the velocity squared. v[sup]2[/sup]/2 + rho g h + p = constant. We can rewrite this as v[sup]2[/sup]/2 = p. Therefore, if we double the pressure, we’re not going to see a doubling of the velocity. Aerodynamic drag works the same why, and is the reason it gets harder and harder to go faster through the air as you go faster and faster.

I wouldn’t be surprised if the relationship is a squared one - so many things in physics have a squared factor in their relationship.

However, it may change things to know what the pressure relates to on the setting. My best guess is that it is the pressure generated from the fluid pump that spins the impeller which creates the current. In this case, the higher pressure in the ‘back end’ fluid line spins the impeller faster, resulting in the faster current that you must swim against.

I have kinda been planning on visiting a local YMCA as a guest and doing a pool workout there to get an idea of calibration (I need an estimated time of completion for the swim portion of a sprint tri) - so I was hoping maybe someone on the list has already done that