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10/44 is a 23% increase in flow rate. Pressure drop goes as the square of the flow change, or 1.23 squared = 1.51. That means pressure drop would increase 51%, so your increase from 3.5 kg/cm2 to 5.0 kg/cm2 is not unreasonable, though still higher than expected. A 1.5 kg/cm2 DP increase would mean the DP prior to the rate increase was 3.0 kg/cm2, which only leaves 0.5 kg/cm2 (~7 psig) for coke drum back pressure, which is unreasonably low. Possibly coke has spalled and is creating additional pressure drop in the piping circuit.

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