Bernoulli's Principle: a Paint Sprayer Pumps Air Through a Constriction

Multiple Choice

Bernoulli's principle: A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m³, and the density of the paint is 1200 kg/m³. We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate?

A) 8.07 mm
B) 4.05 mm
C) 12.2 mm
D) 9.65 mm
E) 14.3 mm