# TAMU CHEN 304 - Class3 (12 pages)

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## Class3

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## Class3

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Pages:
12
School:
Texas A&M University
Course:
Chen 304 - Chem Engr Fluid Ops
##### Chem Engr Fluid Ops Documents
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Department of Chemical and Biological Engineering CBE 341 Mass Momentum and Energy Transport Fall 2017 Lecture 3 09 17 17 Prof P T Brun 1 Problems of practical interest cannot always be solved exactly by analytical methods 2 We wish to conduct as few experiments as possible 3 while working with a suitably scaled model of the geometry of interest 4 expose dimensionless groups or parameters which can be used to correlate the experimental data 5 which allows us to use the correlations across geometric scales 6 examine the exact equations of motion critically By recasting these equations in a dimensionless form one can recognize the relative importance of various terms in the model equations Does not require as a starting point the differential equations describing the evolution of various variables s Dimensionless Groups of Significance in Fluid Mechanics Inertial stress Gravitational stress V 2 Viscous stress gL Interfacial stress V L L The Reynolds number Re is a ratio of the inertial and viscous stresses inertial VL Re viscous The Froude number Fr is taken to be the inertial and gravitational stresses inertial V2 Fr gravitational gL The interfacial stress is also referred to as capillary stress The Weber number We is a ratio of the inertial and interfacial stresses inertial V 2L We interfacial The capillary number Ca is a ratio of the viscous and capillary interfacial stresses viscous V Ca capillary The Bond number Bo is a ratio of the gravitational and interfacial stresses gravitational gL2 Bo interfacial In some problems such as bubbles rising in a liquid one refers to an E tvos number Eo which is a ratio of the buoyancy stress to interfacial stress buoyancy Eo interfacial 2 gL So Eo appears to be very similar to Bond number Here is the density difference

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