I am producing a catalyst that requires high-temperature reduction (500 C) in a Nitrogen environment in a tube furnace. The current setup that I have includes a quartz tube with 20mm (diameter) and 80 mm (working length). The flow rate of Nitrogen is 50 ml/min. Now, we have acquired a bigger furnace and the quartz tube is bigger. 60 mm (diameter) and 300 mm (heated length). I want to know what will be the flow rate of Nitrogen for the bigger quartz tube?
A pipe or tube with a diameter of 20 mm and a length of 80 mm has L/D = 4. As in the turbulent region the friction factor is approximately f = 0.024, the value of K = fL/D = 0.096
For 60 mm of diameter and 300 mm length, L/D = 5 and f = 0.0185, so K is 0.0925 a little less than before.
Therefore, the flow rate will be a little more than before.
While maintaining a constant average speed, the volumetric flow rate should increase ninefold. One can also possibly think of inlet and outlet effects (L/D
Emilio Casado, Your answer is wrong because you only paid attention to the inlet and outlet effects. Do you believe that an increase in tube diameter has no significant effect on the volumetric flow rate of the fluid? The rule is Fv1D12=Fv2D22.
Miroslaw Grzesik, my answer considers only the hydraulic effects on the Nitrogen flow rate when the conditions of the process don´t change. As the question has not more datails, I have assumed that the system has a control that mantain the temperature of the Nitrogen at the end of the tube with the same value as before the tube change.
It´s clear that if you change a furnace tube of 20x80 by other of 60x300, the heating surface, change a lot and without any control, the specific volume of the Nitrogen could increase and therefore decrease the flow rate.
Reduced K (dimensionless resistance coefficient) means the pressure drop (DelP) is lower, so the volumetric flowrate (V_o) is higher
DelP=K*rho*(u^2/2)
m=rho*V_o*pii*(D^2/4)
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