At the same length and PRMs, 1/2 inch tubing carries _____ times more flow than 1/4 inch tubing.

When considering the flow rates of different diameters of tubing, it's important to understand how the cross-sectional area affects the flow capacity. The flow rate through a cylindrical tube is governed by the Hagen-Poiseuille equation for laminar flow and is influenced significantly by the radius of the tubing.

The radius of the 1/2 inch tubing is half an inch, and the radius of the 1/4 inch tubing is a quarter inch. When calculating the flow capacity, we compare their cross-sectional areas, which are proportional to the square of the radius. The area for a cylinder is given by the formula A = πr².

For 1/2 inch tubing:

• Radius = 1/4 inch

• Area = π(1/4)² = π/16

For 1/4 inch tubing:

• Radius = 1/8 inch

• Area = π(1/8)² = π/64

When you compare the two cross-sectional areas, the flow capacity of the 1/2 inch tubing is:

Area_1/2 = π/16

Area_1/4 = π/64

Now, to determine how many times more flow the 1/2 inch tubing carries