Type III problems are not that common. The questions is generally started when we wonder the recommended pipe size (pipe diameter) for a given pressure drop or a friction loss. It get’s worst when you gotta change the diameter of different pipes (i.e. 2 in diameter for the 10 ft. pipe and 3 in for the 15 ft pipe)

In Type III problem, it is impossible to solve algebraically. Many variables depend on the velocity of the fluid.

Velocity can’t be obtained with Q/A = V … since Area is dependent of Diameter
Velocities can’t be related with the diameter sizing VaDa^2 = VbDb^2 (velocity and diameter are not known)
Reynolds Number can’t be calculated directly Re = rho*V*D/miu (velocity and diameter are not known)
Relative Roughness can’t be calculated since D is a factor: e/D
Velocity heads can’t be calculated Va^2 / 2 and Vb^2 / 2
Friction Factor can’t be found with Moody’s Diagram (Re, e/D)
Friction loss is calculated since everything is known
We gotta iterate. Guess for a velocity, typically 1 m/s, then calculate the Area (given a Volumetric Flow Rate). Afterwards, calculate All other equations that depend of Velocity and Diameter (Re, f.f., friction loss, etc.)

If Equation 1 makes sense with the value of the pressure drop or the friction loss. You win! IF not, iterate another value of velocity!

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