Transport phenomena notes

transport phenomena

DIMENSION ANALYSIS

For the introduction he only told about the uses of DIMENSION ANALYSIS which all of us knows and if ne1 wants it then please let me knw(SAURABH)….

k one thing which he mentioned was about DIMENSIONLESS GROUPS…..

DIMENSIONLESS GROUPS = Group of symbols may be put together , either by theory or based on experiment, that have no net units , these are called dimensionless groups.

No. of dimensionless groups = (No. of variables) – (No. of fundamental dimensions)

eg:   REYNOLD’S NUMBER

STANDARD AND OTHER SYSTEM OF UNITS

———–>    WHAT IS “SLUG“????

SLUG is a unit of MASS in the BRITISH ENGINEERING SYSTEM!!!!

BRITISH ENGINEERING SYSTEM:

In this system MASS is not a FUMDAMENTAL DIMENSION whereas FORCE is a FUNDAMENTAL DIMENSION…..

MASS is derived!!!!

Dimensions used in this system:

L                 F                 T

ft                lb_f s         (ft=feet    lbf=pound force   s=seconds)

1 slug = 1 lb_f / (1 ft/s²)

—-> FOR 1 lb of mass, 1 lb_f force produces 32.1740 ft/s² acceleration

FTS :

In this system FORCE is not a FUMDAMENTAL DIMENSION whereas MASS is a FUNDAMENTAL DIMENSION…..

FORCE is derived!!!!

Dimensions used in this system:

L                 M                 T

ft                 lb                  s       (ft=feet    lb=pound   s=seconds)

—-> FOR 1 lb of mass, 1 POUNDAL produces 1 ft/s² acceleration

where POUNDAL is the force….

F (Pound Force) = ( MASS (Pound) x ACCELERATION (ft/s²) ) / g_c

Pound weight force = Pound force ………..(where g = 32.1740 ft/s²)

Normally in various books problems are solved by using both ‘g_c’ and ‘g’….

Where, g = g_c/32.1740

if you have ne correction to be made in this then please let me know(SAURABH SURYAWANSHI)

Added section:-

Generally to increase the no of dimensions and to differentiate between various entities of same units, L is taken as a vector and is expressed in terms of  (Lx ,Ly,Lz)

work:- M Lx  T^-2  Lx

Torque:- M  Lx  T^-2  Ly

angular velocity:- (Lx/Ly) T^-1

frequency:- T^-1

Shear stress:- F/ Lx  Ly^1/2  Lz^1/2

Scaling of   degree R, degree F, degree C and Kelvin(K) :-

100 delta(degree C) = 180 delta(degree F)

same is for K and degree R

The relation between R and K :- [note: scaling and relation are different terms dont mix them up]

R = 1.8 K

If there are any corrections and suggestions for added section contact me(shail)