C1_Introduction - PGE 381M Transport Phenomena Introduction...

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PGE 381M Transport Phenomena
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Introduction Unit system Unit system used in this course: International System of Units Primary (fundamental) units: Mass: kg Length: m •T i m e : s e c Temperature (added for the convenience of expressing thermal units): 0 C Mole (for system with chemical reactions): mole Secondary (derived) derived units Force: N or kg m/s 2 •S t r e s s : N / m 2 or kg /m s 2 Pressure: Pascal (Pa) or kg /m s 2 Viscosity: Pa-s or kg /m s Energy: Joule or kg m 2 /s 2 Power: Watt or kg m 2 /s 3
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Introduction Dimensional analysis Dimension notations • Mass: M • Length: L •Time: t Dimensional analysis • An example: consider steady-state flow in a circular pipe, it is found experimentally that the pressure drop over the pipe length is a function of pipe diameter (d), pipe length (l), velocity (u), fluid density ( ρ ), and fluid viscosity (μ). 1 (, ,, , ) Pf d l u ρµ = How many experiments we need to quantify the sensitivity of the pressure drop to these quantities? To reduce the number of variables, thus of experiments, we need to group these quantities into dimensionless groups. Here is one of the commonly used methods.
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Introduction Dimensional analysis Let postulate the following form of the function f 1 n1 n2 n3 n4 n5 PC d lu ρ µ ∆= ()() ( )( ) ( ) n1 n2 -1 -2 -3 1 M L T L L L t M L t ⇔≡ 45 123 35 M 1 L 3 t nn nnn nn =+
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C1_Introduction - PGE 381M Transport Phenomena Introduction...

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