Page 47 - Fluid mechanics, heat transfer, and mass transfer

FLUID FLOW
24

Reynolds number demonstration experiment.
FIGURE 2.3

or other tracer near the inlet at the center of the pipe & The equation for acoustic velocity is
by means of a hypodermic needle. Flow rates are
0:5
measured by weighing liquid, noting reading of a c ¼ðk b =rÞ ; ð2:6Þ
stopwatch. For each flow rate, Reynolds number is
calculated. where c is the acoustic velocity (m/s), k b is the bulk
3
2
9
& The onset of turbulent flow is identified and Reynolds modulus ( 10 N/m ), and r is the density (kg/m ).
number is determined at the onset. Observations are & This equation is valid for liquids, solids, and gases.
made repeating the experiment for all the pipes. & Sound travels faster through media with higher elas-
Transition Reynolds numbers are calculated. Results
ticity and/or lower density.
show different onsets based on diameters and
. What is equivalent diameter?
roughness.
& Equivalent diameter for flow through a conduit is
. What is meant by fully developed flow? What is tran-
defined as 4(cross-sectional area for flow through the
sition length?
conduit)/wetted perimeter. For a circular conduit,
& When a fluid is flowing through a pipe, obstructions
and cross-section and direction changes can result in 2
equivalent diameter ¼ 4ðpD =4Þ=pD ¼ D; ð2:7Þ
variations in flow velocities and flow profiles. The
laminar or turbulent flow criteria in terms of N Re can
that is, the diameter of the pipe.
be in error. In fully developed flow, the distortions
& Equivalent diameter is used for N Re calculations in
will be absent.
noncircular conduits, annular flow such as flow
& The length of obstructionless pipe to restore fully
through the annulus of a double pipe heat exchange,
developed flow is called the transition length.
shell side flow in shell and tube heat exchanger,
. What is Stokes flow?
packed bed flows, and so on.
& Stokes flow is a type of flow where inertial forces are
. Calculate the equivalent diameter for the annulus of a
small compared to viscous forces. The Reynolds
pipe. What are the equivalent diameters for a rectan-
number is low. This is a typical situation in flows
gular and a square duct?
where the fluid velocities are very low and the
& Figure 2.4 shows annulus of a concentric double
viscosities are very high, as in the case of flow of
pipe.
viscous polymers.
& Annulus:
. What is acoustic velocity? Give the equation.
& The technical definition of acoustic velocity is the 2 2
cross-sectional area of annulus ¼ðpD =4Þ ðpd =4Þ
rate at which a pressure disturbance travels within a 2 2
fluid. Typical acoustic velocities for air and water at ¼ pðD d Þ=4; wetted perimeter ¼ pðD þ dÞ;

20 C are 343.1 and 1481 m/s, respectively. ð2:8Þ