Page 49 - Fluid mechanics, heat transfer, and mass transfer

FLUID FLOW
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is important to note that the only cause of the change the conduit at points 1 and 2, between which flow
in fluid velocity is the difference in balanced pressure continuity exists.
on either side of it. & If the fluid density is different at points 1 and 2, the
. Write Bernoulli’s equation for unit mass, unit length, mass flow rate is given by
and unit volume of the fluid.
& For incompressible flow in a uniform gravitational m ¼ V 1 A 1 r ¼ V 2 A 2 r : ð2:19Þ
2
1
field, Bernoulli’s equation can be written as
2
v =2 þ gh þ p=r ¼ constant; ð2:17Þ . What is Venturi effect?
& The Venturi effect is an example involving appli-
where v is the fluid velocity along the streamline, g is
cation of Bernoulli’s principle, in the case of a fluid
the acceleration due to gravity, h is the height of the
flowing through a tube or pipe with a constriction in
fluid, p is the pressure along the streamline, and r is
it. The fluid velocity must increase through the
the density of the fluid.
constriction to satisfy the equation of continuity,
. What are the assumptions involved in Bernoulli’s
while its pressure must decrease due to conserva-
equation?
tion of energy. The gain in kinetic energy is sup-
& Flow is inviscid, that is, viscosity of the fluid is zero.
plied by a drop in pressure or a pressure gradient
& Steady-state incompressible flow. force.
& In general, the equation applies along a streamline. . Define skin and form friction.
For constant density potential flow, it applies & Skin friction is due to viscous drag.
throughout the entire flow field. & Form friction is the drag due to pressure distribution.
& Density, r, is constant, though it may vary from
. What is drag? Explain.
streamline to streamline.
& Drag is a force on a body due to a moving fluid
. What are velocity head and pressure head?
interacting with it. Drag force slows down the flow-
2
& The term v /2g is called the velocity head and p/rg is ing fluid, causes push of the object directly down-
called the pressure head. stream, and transfers downstream momentum to the
. Give an example of the utility of the velocity head object.
concept. & Drag is a function of the body shape over which fluid
& It is used, for example, for sizing the holes in a is flowing. Different shapes will cause the flow to
sparger, calculating leakage through a small hole, accelerate around them differently, that is, stream-
sizing a restriction orifice, and calculating the flow lined shapes. Low drag shapes: gentle curves; con-
with a pitot tube and the like. tinuous surfaces prevent flow separation (reduce
& With a coefficient, it is used for orifice calculations, wake). The shape of an object has a very large effect
relating fitting losses, relief valve sizing, and heat on the magnitude of drag.
exchanger tube leak calculations. & Figure 2.6 gives drag coefficients for different shapes
. “The velocity head concept is used in sizing holes in a of objects.
sparger.” True/False? & AquickcomparisonoftheshapesshowninFigure2.6
& True. For a sparger consisting of a large pipe having shows that a flat plate gives the highest drag and a
small holes drilled along its length, the velocity head streamlined symmetric airfoil gives the lowest drag,
concept applies directly, because the hole diameter by a factor of almost 30. Shape has a very large effect
and the length of fluid travel passing through the hole on the amount of drag produced.
have similar dimensions. An orifice, on the other & The drag coefficient for a sphere is given with a range
hand, needs a coefficient in the velocity head equa- of values because the drag on a sphere is highly
tion because the hole diameter has a much larger dependent on Reynolds number.
dimension than the length of travel through the & Flow past a sphere, or cylinder, goes through a
orifice, that is, through the thickness of the orifice. number of transitions with velocity. At very low
. Write the continuity equation. velocity, a stable pair of vortices is formed on the
downstream side.
Q ¼ V 1 A 1 ¼ V 2 A 2 ; ð2:18Þ & As velocity increases, the vortices become unstable
and are alternately shed downstream. Further in-
where Q is the volumetric flow rate, V is the flow crease in velocity results in the boundary layer
velocity, and A 1 and A 2 are cross-sectional areas of transitions to chaotic turbulent flow with vortices of