Page 186 - Mechanical Engineers' Handbook (Volume 2)

9 Flow Rate 175

W mass flow rate, lb /min or kg/s
m
3
3
Q volume flow rate, ft /min or m /s
Also frequently used:
GPM gallons per minute
CFM cubic feet per minute
3
ACFM actual cubic feet per minute, ft /min
SCFM standard cubic feet per minute, ft /min
3
Consider a flowmeter operating at 2 atm and 70 F. The density of a gas at those con-
ditions is twice its density at standard conditions. Consider a flow through the meter such
that 100 ft of gas at 70 F and 2 atm passes through the meter each minute. This 100 ft of
3
3
gas would occupy 200 ft if it were at standard conditions. In this case, the flow rate could
3
be described either as 100 ACFM (at 70 F and 2 atm) or 200 SCFM. If ACFM is quoted,
then the temperature and pressure must also be specified. The term SCFM describes the mass
flow but expresses it in terms of the volume that that mass flow would occupy if it were at
standard conditions.

9.2 Basic Principles Used in Flow Measurement

Measurement of flow rate can be accomplished using many different physical principles.
The basic flow rate equation is
W AV (25)

where W flow rate, lb /s (kg/s)
m
2
2
A area, ft (m )
V velocity, ft/s (m/s)
3
3
density, lb /ft (kg/m )
m
To measure flow, any metering system must provide enough information to evaluate all
three terms. Usually, two of the terms are fixed, and flow is evaluated by observing the
change in the remaining term. An orifice used on water (presumed to be constant density)
fixes A and , leaving W proportional to V. A variable-area meter fixes and V, leaving W
proportional to A. Any combination of physical laws that permits evaluation of , A, and V
can form the basis for a flow-metering system.
Flowmeters can be divided into three generic groups depending on their sensing prin-
ciple: conservation based, rate based, and dynamic.
The first group consists of flowmeters which depend upon a conservation principle for
their output. There are three conservation laws which can be related to mass flow: conser-
vation of mass, conservation of momentum, and conservation of energy. Conservation of
momentum provides the basis for a large class of meters: orifices, nozzles, Venturi meters,
drag disks, and obstruction meters. Conservation of energy (usually thermal energy) has been
used in the construction of flowmeters for small flow rate. The conservation-of-mass law is
used implicitly in all systems.
The second large group of flowmeters depend upon rate equations. There are many
natural phenomena whose rate depends upon fluid velocity: viscous drag, heat transfer, mass
transfer, displacement of a tracer particle, and so on. Any rate process sensitive to flow rate
can be used as the basis for a flowmeter.