$4.(10$ points$)$ A venturi meter is used to measure air velocity. A one$-$fifth scale model of the venturi meter is built, and water is used as the test fluid. Assume water is at $15\mathrm{.}6$ C and air is approximately the same temperature.

a$.$ If use of a venturi meter implies pipe flow, what common dimensionless group should be used to perform a scaling analysis?

b$.$ Use your answer from $($a$)$ to determine an expression for the approximate ratio of the model velocity to the air velocity in the full$-$scale meter.

The correct answer is a ratio of $0\mathrm{.}039$