Page 26 - Fluid mechanics, heat transfer, and mass transfer

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FLUID MECHANICS BASICS

1.1 Dimensional Analysis 3 & In such situations involving four or more variables,
1.2 Fluid Properties 4 dimensional analysis becomes a necessity as correla-
1.3 Newtonian and Non-Newtonian Fluids 5 tions progressively become very complex.
1.4 Viscosity Measurement 8
. Name the dimensionless numbers of significance in
1.5 Fluid Statics 10
fluid mechanics. Give their physical significance.
1.5.1 Liquid Level 15
& Reynolds number, N Re ¼ DVr/m ¼ inertial forces/
viscous forces.
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& Weber number, N We ¼ LV r/s ¼ inertial forces/
surface tension forces. L is the characteristic length
and s is surface tension. It can be considered as a
measure of the relative importance of the inertia of
1.1 DIMENSIONAL ANALYSIS
the fluid compared to its surface tension. It is useful in
. Differentiate between units and dimensions by means of analyzing thin film flows and the formation of dro-
examples. plets and bubbles.
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& Examples of dimensions include weight, time, & Froude number, N Fr ¼ V /Lg ¼ inertial forces/
length, and so on. gravity forces. In the study of stirred tanks, the
Froude number governs the formation of surface
& Examples of units include seconds, days, years,
vortices. Since the impeller tip velocity is propor-
inches, centimeters, kilometers, grams, pounds, and
tional to ND, where N is the impeller speed (rev/s)
so on.
and D is the impeller diameter, the Froude number
. What are the methods used to carry out dimensional 2
then takes the form Fr ¼ N D/g.
analysis?
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& Euler number, N Eu ¼ ( DP)/rV ¼ frictional pres-
& Rayleigh’s method.
sure loss/(2 velocity head).
& Buckingham p-theorem. 0 2
& Critical cavitation number, s ¼ (P P )/(rV /2) ¼
. Under what circumstances dimensional analysis be-
excess pressure above vapor pressure/velocity
comes a tool for obtaining solutions to problems?
head. Cavitation number is useful for analyzing fluid
& When two variables are to be correlated, a simple plot
flow dynamics problems where cavitation may occur.
of one variable versus the other will describe the & Cauchynumber,C ¼ rv /b ¼ inertialforce/compress-
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problem.
ibility force. v is the local fluid velocity (m/s) and b is
& When three variables are to be correlated, for each
the bulk modulus of elasticity (Pa). Cauchy number is
value of the third variable, a plot of the other two as in defined as the ratio between inertial force and the
the above case will describe the problem; that is, a compressibilityforce (elasticforce) ina flow. Itis used
number of plots, each for one value of the third in the study of compressible flows. Cauchy number is
variable, will be required. related to Mach number. It is equal to square of the
& When more than three variables are involved in a Mach number for isentropic flow of a perfect gas.
correlation, the correlation becomes complex & Capillary number, Ca ¼ mV/r ¼ viscous force/
and requires a set of curves for each of the fourth surface tension force. Capillary number represents
variable. the relative effect of viscous forces versus surface
Fluid Mechanics, Heat Transfer, and Mass Transfer: Chemical Engineering Practice, By K. S. N. Raju
Copyright Ó 2011 John Wiley & Sons, Inc.

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