Project ForgeMass Transfer
Diffusion
GATE 2013
Hard
A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation Sh=0.025Re^0.6·Sc^0.33. If the velocity of the fluid and the diameter of the pipe are both doubled, what is the new value of kc in mm/s, up to 2 digits after the decimal point?
1.15 mm/s(± 0.05 accepted)
Explanation
kc=Sh·D/d ∝ Re^0.6/d ∝ (Vd)^0.6/d = V^0.6·d^(−0.4) (properties, hence Sc, unchanged). If both V and d double: kc,new/kc,old=2^0.6×2^(−0.4)=2^0.2≈1.1487. kc,new=1×1.1487≈1.15 mm/s.
Source: GATE CH 2013 (2013)
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