For many years differential pressure types of flowmeters have been the most
widely applied flow rate measuring device for fluid flows in pipes that require
accurate measurement at reasonable cost. Although a number of different types of
flow rate-measuring devices are now available, the differential pressure type of
flowmeter still makes up the largest segment of the total flow measurement market.

This type of device has a flow restriction in the line that causes a differential
pressure or "head" between the two measurement locations. The differential pressure
between two specified locations relates to the flow rates through the pipe.
Differential pressure flowmeters are also known as head-type meters, and, of all
the head-type meters, the orifice flowmeter is the most widely applied device. Italian
physicist Giovanni B. Venturi (1746-1822) in 1797 performed the first
recorded work that used orifices for the measurement of fluid flows.

Operating Principle

Differential pressure flowmeters have a change in flow cross-section that can
be described as a restriction placed in the flow line that causes the velocity of the
flowing fluid to change. The difference in pressures between the two measurement
locations of the flowmeter is the result of the change in the flow velocities.
The volume flow rate through the cross-sectional area is given by,

Advantages:

• Simple construction
• Relatively inexpensive
• No moving parts
• Transmitting
  instruments are external
• Low maintenance
• Wide application of flowing fluid
• Ease of instrument
  and range selection
• Extensive product
  experience and
  performance data base
• An abundance of application and selection guides
• Readily available
  standards and codes of practice

Using Equation (8-1) and the theory of conservation of mass, the equation of
continuity states the relationship between the velocity and fluid flows for
incompressible fluid in a closed conduit as:

Disadvantages:

• Flow rate is a
  nonlinear function of the differential
  pressure
• Low flow rate rangeability
  with normal
  instrumentation

where the subscripts refer to the cross sections 1 and 2 of Figure 8-1. For ideal
fluid (no frictional losses), Bernouli's equation states that the sum of the static
energy (pressure head), the kinetic energy (velocity head), and the potential
energy (elevation head) of the fluid is conserved in the flow across a constriction
in a pipe.