EternityForest:
I think the water columb rate should be pretty linear if the source pressure is high enough. I imagine that it would be similar to charging a capacitor through a resistor. 2 feet of water is about 1psi.The real issue is consistancy between the tubes for a fair race.
However, if you fill by pouring from the top the pressure issue goes away. You would still need a little valve on each to calibrate the fill rates.
I think the issue is that if you open a valve as suggested (not pumping it), the column will equal out as fast as possible, driven by the pressure difference across the orifice plate. As the pressure on the "score" column rises, the pressure differential will drop, as will the rate. Just rearrange the Bernoulli equation and you've got your volumetric flow rate, Q = A2 * sqrt(1/((1-d2/d1)^4)) * sqrt(2*(P1-P2)/rho), where A2 is the "score" pipe diameter, d2 is the orifice diameter, d1 is the input pipe diameter, and P1 and P2 are pressures on respective sides of the orifice plate. Graphing that you, you'll see that the rate of rise will be quite different over time as the pressures equalize.
Honestly I'm more of a fluids guy than an electrical guy, so I'm not sure how this compares to the equation for charging a capacitor through a resistor, though I'm familiar with the concept.