Page 46 - Fluid mechanics, heat transfer, and mass transfer

FLOW PHENOMENA 23

where v is the velocity at a pipe radius of r, V is the & True. Effects of viscosity are manifest only in a thin
average velocity (Q/A), which is the equation for a layer near the surface where steep velocity gradients
parabola, and R is the radius of the pipe. occur.
& Average velocity for laminar flow is 0.5 of maximum . “Velocity profile of Newtonian fluids in laminar flow is
velocity in the centerline. The velocity profile is flatter than that in turbulent flow.” True/False?
parabolic, the gradient of which depends on the & False.
viscosity of the fluid for a set flow rate. . “Maximum velocity of Newtonian fluids in laminar
& Average velocity for turbulent flow depends on N Re .
flow inside a circular pipe is twice the average velocity.”
For N Re of 5000, it is equal to 0.77 and for N Re of True/False?
6
3 10 it is equal to 0.87 of maximum velocity in the & True.
centerline (logarithmic profile).
. What criteria can be adopted for pressure drop calcula-
& Turbulent Flow: For rough pipes in turbulent flow,
tions in laminar to turbulent flow conditions in pipeline
velocity profile is much more flattened than in the
flow?
case of laminar flow and is given by
& In transition flow range, frictional losses should be
calculated based on both laminar and turbulent con-
u þ ¼ 2:5lnðy=«Þþ 8:5 for y þ > 30; ð2:4Þ
ditions and the highest resulting loss should be used
p in subsequent system calculations.
where u þ is v/u (dimensionless), u ¼ (t w /r),
. What is potential flow?
which is called friction velocity, and t w is the
2
wall stress given by frV =2 ¼ DP/4L for a circular & Flow behavior strongly depends on the influence of
pipe. y þ is the dimensionless distance from the wall solid boundaries.
(¼yu r/m). & If the influence of solid boundary is negligible or
small, shear stress may be negligible and the fluid
v av ¼ 0:5v max : ð2:5Þ behavior approaches zero viscosity, that is, inviscid.
& This type of flow is called potential flow.
& As the liquid enters the pipe, its profile will be more . Why the discharge ends of the pipes are elevated
blunt due to a smaller difference in velocity between compared to the test pipes in a pipe friction experiment?
its outer layers and those toward the center. & This arrangement ensures that the pipe is full, water
& This flow pattern, and the resulting friction, is due to
occupying the entire cross section.
the rather complex interactions of the forces of . What is superficial velocity?
adhesion and cohesion and the momentum of the
& Superficial velocity is defined as volumetric flow rate
moving liquid.
divided by cross-sectional area for flow.
& Figure 2.2 illustrates the velocity profiles for laminar
. What is mass velocity?
and turbulent flows.
& Mass velocity, G, is defined as mass flow rate divided
. What types of velocity profiles develop for liquid metal
by cross-sectional area for flow, G ¼ Vr.
flow in pipes?
. How and why a Reynolds number experiment is carried
& Velocity profiles for liquid metal flow will be flatter
out?
than those for turbulent flow and velocities are
& A Reynolds number experiment (Figure 2.3) is car-
practically constant along the radius of the pipe from
ried out in pipe flows with different diameter pipes,
center to the wall.
smooth and rough. Flow is gradually varied, visually
. “Flow far from the surface of a solid object is inviscid.”
observing flow streamlines by injecting a dye or ink
True/False?

FIGURE 2.2 Velocity profiles for laminar and turbulent flows.