The Three Flow Problems

The friction factor relates six parameters of the flow:

1. Pipe diameter (\(D\))
   
2. Average velocity (\(v\))
3. Fluid density (\(\rho\))
4. Fluid viscosity (\(\mu\))
5. Pipe roughness (\(k\))
6. The frictional pressure drop (\(\Delta P_f\))

Therefore, given any five of these, we can use the friction-factor charts to find the sixth.

Most often, instead of being interested in the average velocity, we are interested in the volumetric flow rate \(Q = (\pi/4)D^2v\)

The three most common types of problems are the following:

Generally, type 1 can be solved directly, where as types 2 and 3 require simple trial and error.

1. Given \(D\), and \(v\) or \(Q\), compute the pressure drop. (pressure-drop problem)
2. Given \(D, \Delta P_f\), compute velocity or flow rate (flow-rate problem)
3. Given \(Q, \Delta P_f\), compute the diameter (\(D\)) of the pipe (sizing problem)