### The Three Flow Problems

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The friction factor relates six parameters of the flow:

1. Pipe diameter
2. Average velocity
3. Fluid density
4. Fluid viscosity
5. Pipe roughness
6. The frictional losses per unit mass.

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 = (p/4)D2V

The three most common types of problems are the following:

 Type Given To find 1 D, k, r, m, Q hf 2 D, k, r, m, hf Q 3 k, r, m, hf, Q D

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

Three fundamental problems which are commonly encountered in pipe-flow calculations: Constants: r, m, g, L
1. Given D, and v or Q, compute the pressure drop. (pressure-drop problem)
2. Given D, delP, compute velocity or flow rate (flow-rate problem)
3. Given Q, delP, compute the diameter D of the pipe (sizing problem)