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Measurement Of Flow Rate Through Pipe
Flow rate through a pipe is usually measured by providing a coaxial area
contraction within the pipe and by recording the pressure drop across the
contraction. Therefore the determination of the flow rate from the measurement
of pressure drop depends on the straight forward application of
Bernoulli’s equation. Three different flow meters operate on this principle.
- Venturimeter
- Orificemeter
- Flow nozzle.
Venturimeter
A venturimeter is essentially a short pipe (Fig. 5.1l) consisting of two conical
parts with a short portion of uniform cross-section in between. This short
portion has the minimum area and is known as the throat. The two conical
portions have the same base diameter, but one is having a shorter length with
a larger cone angle while the other is having a larger length with a smaller
cone angle.
Fig 14.1 A Venturimeter
The venturimeter is always used in a way that the upstream part of the flow
takes place through the short conical portion while the downstream part
of the flow through the long one. This ensures a rapid converging passage
and a gradual diverging passage in the direction of flow to avoid the loss of
energy due to separation. In course of a flow through the converging part,
the velocity increases in the direction of flow according to the principle of
continuity, while the pressure decreases according to Bernoulli’s theorem.
The velocity reaches its maximum value and pressure reaches its minimum
value at the throat. Subsequently, a decrease in the velocity and an increase
in the pressure take place in course of flow through the divergent part. This
typical variation of fluid velocity and pressure by allowing it to flow through
such a constricted convergent-divergent passage was first demonstrated by
an Italian scientist Giovanni Battista Venturi in 1797.
Fig 14.2 Measurement of Flow by a Venturimeter
Figure 14.2 shows that a venturimeter is inserted in an inclined pipe line in
a vertical plane to measure the flow rate through the pipe. Let us consider a
steady, ideal and one dimensional (along the axis of the venturi meter) flow
of fluid. Under this situation, the velocity and pressure at any section will
be uniform. Let the velocity and pressure at the inlet (Sec. 1) are V1 and p1
respectively, while those at the throat (Sec. 2) are V2 and p2. Now, applying
Bernoulli’s equation between Secs 1 and 2, we get
 (14.1)
 (14.2)
where ρ is the density of fluid flowing through the venturimeter. From continuity,
 (14.3)
where A1 and A2 are the cross-sectional areas of the venturi meter at its throat and inlet respectively. With the help of Eq. (14.3), Eq. (14.2) can be
written as
 (14.4)
where  and  are the piezometric pressure heads respectively, and are
defined as
 (14.5a)
 (14.5b)
Hence, the volume flow rate through the pipe is given by
 (14.6)
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