A prototype 90 degree pipe elbow has ethyl alcohol at 20 degrees Celsius flowing through it. The pressure drop through the elbow of 150 mm diameter for flow at 1.5 m/s is unknown. The radius of curvature of the elbow is 1 m.
Tests on a geometrically-scaled model elbow will use water at 20 degrees Celsius at 4 m/s. Find the diameter and radius of curvature of the model elbow for dynamic similarity. Show the details of your dimensional analysis. Compute the pressure drop through the prototype elbow is the pressure drop in the model is 18 kPa.