Dear Shaber,

In addition like mentioned by MoverZ, limitation of vertical deflection is based on to avoid resonance. For resonance issue, pipe quite stiff for small deflection = high natural frequency. It purpose is to avoid large amplitude due to small disturbing force.

fn = 1/2*phi *(g/deflection)^0.5 = 3.12/(deflection)^0.5
Deflection = 3.12/fn ; fn = natural frequency ; g = acceleration of gravity.

Let say that 4 cps is the sufficient natural frequency. We can solve the deflection = 0.78 in. Then by using formula deflection in the middle of pipe then solve for L = distance of span = (deflection*E*I/22.5w)^0.5

Please note that the shorter span will give higher natural frequency. But natural frequency not need to be so high, 4 cps is quite good. You can take as reference "Introduction to Pipe Stress Analysis" by Sam Kannapan Chapter III - Pipe Span Calculation.