fluid_mechanics

8.6 Pipe Flowrate Measurement 441
F I G U R E 8.38
pipe network.
A general
be obtained. Of course, trial-and-error solutions are usually required because the direction of flow
and the friction factors may not be known. Such a solution procedure using matrix techniques is ideally
suited for computer use 1Refs. 21, 222.
8.6 Pipe Flowrate Measurement
It is often necessary to determine experimentally the flowrate in a pipe. In Chapter 3 we introduced
various types of flow-measuring devices 1Venturi meter, nozzle meter, orifice meter, etc.2 and discussed
their operation under the assumption that viscous effects were not important. In this section
we will indicate how to account for the ever-present viscous effects in these flow meters. We will
also indicate other types of commonly used flow meters.
Orifice, nozzle and
Venturi meters
involve the concept
“high velocity gives
low pressure.”
8.6.1 Pipe Flowrate Meters
Three of the most common devices used to measure the instantaneous flowrate in pipes are the orifice
meter, the nozzle meter, and the Venturi meter. As was discussed in Section 3.6.3, each of these
meters operates on the principle that a decrease in flow area in a pipe causes an increase in velocity
that is accompanied by a decrease in pressure. Correlation of the pressure difference with the
velocity provides a means of measuring the flowrate. In the absence of viscous effects and under
the assumption of a horizontal pipe, application of the Bernoulli equation 1Eq. 3.72 between points
112 and 122 shown in Fig. 8.39 gave
Q ideal A 2 V 2 A 2 B
21 p 1 p 2 2
r11 b 4 2
(8.37)
where b D 2D 1 . Based on the results of the previous sections of this chapter, we anticipate that
there is a head loss between 112 and 122 so that the governing equations become
and
Q A 1 V 1 A 2 V 2
p 1
g V 2 1
2g p 2
g V 2 2
2g h L
The ideal situation has h L 0 and results in Eq. 8.37. The difficulty in including the head loss is
that there is no accurate expression for it. The net result is that empirical coefficients are used in
the flowrate equations to account for the complex real-world effects brought on by the nonzero
viscosity. The coefficients are discussed in this section.
Q
V 1
D 1 (2)
V 2
(1)
D 2
F I G U R E 8.39
pipe flow meter geometry.
Typical