The volumetric flow Q through a pipe containing a sharp-edged orifice is known to depend on the diameter of the pipe, D; the diameter of the orifice, d; the density, ? and dynamic viscosity, ? , of the fluid flowing through the pipe; and the pressure drop across the orifice, ?p.
a) Develop the dimensionless groups that are relevant for this problem using density, pipe diameter, and viscosity as the repeating variables (a wise choice).
b) Develop the dimensionless groups that are relevant for this problem using pipe diameter, pressure drop, and viscosity as the repeating variables. Show that there is a problem with eliminating the remaining variables when using the procedure outlined in class (by inspection).
c) Instead, use the simultaneous equation approach given in the textbook to find the exponents.
d) What happened in part b is one of the few ways that inspectional analysis can breakdown (it started with a poor choice of repeating variables), but it is easy to recognize. In this situation, we can try a different set of repeating variables or use the exponent approach. Alternatively, if we notice that p gives units of Time, we can redo the inspectional analysis. Redo part b using p and show that you will get the equivalent result as in part c.