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Recap
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- The total mechanical energy of a fluid element in an inviscid and irrotational
flow remains the same everywhere in the flow field, while it
does so only along a streamline in an inviscid but rotational flow.
- Flows having only tangential velocities with streamlines as concentric
circles are known as plane circular vortex flows. A free vortex flow is
an irrotational vortex flow where the total mechanical energy of the fluid elements remains same in the entire flow field and the tangential
velocity is inversely proportional to the radius of curvature. A forced
vortex flow is a rotational vortex flow where the tangential velocity
is directly proportional to the radius of curvature. Pressure in vortex flows increases with an increase in the radius of curvature. Spiral vortex flows are obtained as a result of superimposition of a plane circular
vortex flow with a purely radial flow.
- Apart from losses due to friction, the loss of mechanical energy is incurred,
in course of flow through a closed duct, when the path of the fluid stream is suddenly changed due to any abrupt change in the geometry
of the duct. In long ducts, these losses are very small as compared
to the friction loss and hence they are termed as minor losses. These
include (i) losses due to an abrupt enlargement of the cross-section of
a duct, (ii) losses due to an abrupt contraction of the cross-section of
a duct, (iii) losses due to the exist from a small pipe or duct to a large
reservoir, and (iv) losses due to the entrance from a large reservoir to
a small pipe or duct.
- Venturimeter, Orificemeter and Flow nozzle are the typical flow meters
which measure the rate of flow of a fluid through a pipe by providing
a coaxial area contraction within the pipe and thus creating a pressure
drop across the contraction. The flow rate is measured by determining
the velocity of flow at the constricted section in terms of the pressure
drop by the application of Bernoulli’s equation.
- A venturimeter is a short pipe consisting of
two conical parts with a sort uniform cross-section, in between, known
as throat.
- An orificementer is a thin circular plate with a sharp edged
concentric circular hole in it.
- A flow nozzle is a short conical tube providing
only a convergent passage to the flow. In a comparison between
the three flow meters, a venturimeter is the most accurate but the
most expensive, while the orificemeter is the least expensive but the
least accurate. Flow nozzle falls in between these two.
- The static pressure in a fluid is the thermodynamic pressure defining
the state of fluid and becomes equal to the arithmetic average of the
normal stresses at a point in case of a real and Stoksian fluid. The
stagnation pressure at a point in a fluid flow is the pressure which could
result if the fluid were brought to rest isentropically. The difference
between the stagnation and static, pressure is the pressure equivalence
of the velocity head ( 1/
2ρV 2) and is known as dynamic pressure.
- An
instrument which contains tubes to record the stagnation and static
pressures in a flow to finally determine the flow velocity and flow rate
is known as a Pitot static tube.
- An orifice is a small aperture through which the fluid passes. The
liquid from a tank is usually discharged through a small orifice at its
side. A drowned or submerged orifice is one which does not discharge
into open atmosphere, but discharge into liquid of the same kind. The
discharge through an orifice is increased by fitting a short length of
pipe to the outside known as external mouthpiece. The discharge rate
is increased due to a decrease in the pressure at vena contracta within
the mouthpiece resulting in an increase in the effective head causing
the flow.
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Congratulations! you
have finished Chapter 5.
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