That's exactly what we did... used a gallon milk jug with a hose attached, connected to hypodermic needles of various gauges. So, by using the Bernoulli equation, I guess we relied on the average flow velocity, rather than separately considering the more complex equations needed to deal with...
I did an experiement to measure flow rate through a pipe, varying radius and pressure difference. I used Bernoulli's equation (v=√2gh) to compute the velocity of the fluid flow through the pipe, and multiplied the cross sectional area of the pipe (πr^2) by this flow velocity to compute volume...