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Unformatted text preview: viscometer. c. British Standard 188 Falling Sphere Viscometer. d. Any form of Rotational Viscometer Note that this covers the E.C. exam question 6a from the 1987 paper. © D.J.DUNN 7 2. LAMINAR FLOW THEORY The following work only applies to Newtonian fluids.
2.1 LAMINAR FLOW
A stream line is an imaginary line with no flow normal to it, only along it. When the flow is
laminar, the streamlines are parallel and for flow between two parallel surfaces we may consider
the flow as made up of parallel laminar layers. In a pipe these laminar layers are cylindrical and
may be called stream tubes. In laminar flow, no mixing occurs between adjacent layers and it
occurs at low average velocities.
2.2 TURBULENT FLOW
The shearing process causes energy loss and heating of the fluid. This increases with mean
velocity. When a certain critical velocity is exceeded, the streamlines break up and mixing of
the fluid occurs. The diagram illustrates Reynolds coloured ribbon experiment. Coloured dye is
injected into a horizontal flow. When the flow is laminar the dye passes along without mixing
with the water. When the speed of the flow is increased turbulence sets in and the dye mixes
with the surrounding water. One explanation of this transition is that it is necessary to change
the pressure loss into other forms of energy such as angular kinetic energy as indicated by small
eddies in the flow. Fig.2.1
2.3 LAMINAR AND TURBULENT BOUNDARY LAYERS
In chapter 2 it was explained that a boundary layer is the layer in which the velocity grows
from zero at the wall (no slip surface) to 99% of the maximum and the thickness of the layer is
denoted δ. When the flow within the boundary layer becomes turbulent, the shape of the
boundary layers waivers and when diagrams are drawn of turbulent boundary layers, the mean
shape is usually shown. Comparing a laminar and turbulent boundary layer reveals that the
turbulent layer is thinner than the laminar layer. Fig.2.2
© D.J.DUNN 8 2.4 CRITICAL VELOCITY - REYNOLDS NUMBER
When a fluid flows in a pipe at a volumetric flow rate Q m3/s the average velocity is defined um = Q
A A is the cross sectional area. The Reynolds number is defined as R e = ρu m D u m D
ν If you check the units of Re you will see that there are none and that it is a dimensionless
number. You will learn more about such numbers in a later section.
Reynolds discovered that it was possible to predict the velocity or flow rate at which the
transition from laminar to turbulent flow occurred for any Newtonian fluid in any pipe. He also
discovered that the critical velocity at which it changed back again was different. He found that
when the flow was gradually increased, the change from laminar to turbulent always occurred at
a Reynolds number of 2500 and when the flow was gradually reduced it changed back again at a
Reynolds number of 2000. Normally, 2000 is taken as the critical value. WORKED EXAMPLE 2.1
Oil of density 860 kg/m3 has a kinematic viscosity of 40 cSt. Calculate the critical velocity
when it flows in a pipe 50 mm bore diameter.
SOLUTION u mD
R ν 2000x40x10 −6
um = e =
= 1.6 m/s
Re = © D.J.DUNN 9 2.5 DERIVATION OF POISEU...
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- Spring '14