Page 48 - Instrumentation Reference Book 3E

Flow in oDen channels 33

be used to measure gas flows with apparently is given the same form in the horizontal
excellent results. plane as a section of a venturi tube while
In liquid flow mea-surement, even in slurries, the bottom of the channel is given a gen-
Coriolis mass flow meters have nearly completely tle slope up the throat.
replaced other types of mass flow measure- (b) Velocitjdarea method. Where measurement
ments such as dual-turbine, or volumetricidensity of both variables, i.e., head and velocity, is
combinations. combined with the known geometry of a
structure to determine flow.
(c) Dilution gauging.
Pressure-dfferential methods In its classical
form the meter consists of four matched orifice
plates installed in a Wheatstone bridge arrange- 1.4. I Headlarea method
ment. A pump is used to transfer fluid at a known 1.4.1. I Weirs
rate from one branch of the bridge into another to
create a reference flow. The resultant differential Weirs may have a variety of forms and are classi-
pressure measured across the bridge is propor- fied according to the shape of the notch or open-
tional to mass flow rate. ing. The simplest is the rectangular notch, or in
certain cases the square notch.
The V or triangular notch is a V-shaped notch
Thermal mass flowmeter This version of a mass with the apex downwards. It is used to measure
flowmeter consists of a flowtube, an upstream rates of flou7 that may become very small. Owing
and downstream temperature sensor and a heat to the shape of the notch the head is greater at
source as illustrated in Figure 1.44. The tempera- small rates of flow with this type than it would be
ture sensors are effectively active arms of a for the rectangular notch.
Wheatstone bridge. They are mounted equidi- Notches of other forms, which may be trape-
stant from the constant-temperature heat source zoidal or parabolic, are designed so that they
such that for no flow conditions, heat received by have a constant discharge coefficient, or a head
each sensor is the same, and the bridge remains in that is directly proportional to the rate of flow.
balance. However, with increasing flow, the The velocity of the liquid increases as it passes
downstream sensor receives progressively more over the weir because the center of gravity of the
heat than the upstream sensor, causing an imbal- liquid falls. Liquid that was originally at the level
ance to occur in the bridge circuit. The tem- of the surface above the weir can be regarded as
perature difference is proportional to mass flow having fallen to the level of the center or‘ pressure
rate and an electrical output representing this is of the issuing stream. The head of liquid produ-
developed by the bridge circuit. cing the flow is therefore equal to the vertical
This type of mass flowmeter is most commonly distance from the center of pressure of the issuing
applied to the measurement of gas flows within the stream to the level of the surface of the liquid
ranges 2.5 x IO-’’ to 5 x 1V3 kg/s and accuracy upstream.
of il percent of f~~ll scale is attainable. Some If the height of the center of pressure above the
thermal flowmeters are also used for liquid flow sill can be regarded as being a constant fraction of
measurements, including very low flow rates. the height of the surface of the liquid above the
sill of the weir, then the height of the surface
above the sill will give a measure of the differen-
1.4 Fisw in open channels tial pressure producing the flow. If single particles
are considered, some will have fallen a distance
Flow measnrement in open channels is a require- greater than the average b-lt this is compensated
ment normally associated with the water and for by the fact that others have fallen a smaller
wastewater industry. Flow in rivers: sewers distance .
(part-filled pipes), and regular-shaped channels The term “head of a weir” is usually taken to
may be measured by the following methods: mean the same as the depth of the weir, and is
(a) Headlarea m-ethod. Where a structure is built measured by the height of the liquid above the
level of the sill of the weir just upstream of where
into the flowstream to develop a unique head/ it begins to curve over the weir, and is denoted by
flow relationship, as in Hand usually expressed in units of length such as
(i) The weir, which is merely a dam over meters.
which liquid is allowed to flow, the depth
of liquid over the sill of the weir being a
measure of the rate of flow. Rectangular notch Consider the flow over the
(ii) The hydraulic flume, an example being weir in exactly the same way as the flow through
the venturi flume, in which the channel other primary differential-pressure elements. If the