Flow transducers measure the flow of materials in a process. This flow of materials can be in solid, gas, or liquid form. All flow control applications utilize the term Q, or rate of flow, to define flow measurement in the system.
In this section, we will discuss the rate of flow for each kind of material—
solid, liquid, and gas—and the transducers used to measure them.
SOLID FLOW TRANSDUCERS
Solid flow is typically measured with a strain gauge–based load cell trans-ducer, which measures the weight of the product. Solid flow measurement frequently integrates the use of a conveyor or belt product transporter with a load cell. The units generally used for this type of flow measurement are lbs/min or kg/min. Figure 13-27 illustrates an example of how a load cell measures the flow of solids. The equation that describes the flow (Q) is:
Q WV
= L
Figure 13-27. Load cell measuring the flow of solids.
Conveyor Velocity (V)
Weight (W)
Length L
Load Cell Transducer and Signal Conditioning Circuit Hopper
W
V L
EXAMPLE 13-9
A conveyor transports material that is weighed on a platform 2 meters in length. A load cell, which is connected to an analog input module through a bridge circuit and an amplifier, must weigh 50 kgs of the material. The required flow is 1200 kgs/min. Find the speed at which the conveyor must run to obtain the required flow. Also, suggest how to control the conveyor so that the flow rate remains constant.
SOLUTION
The velocity of the conveyor is expressed as:
Q WV
L
V QL
W
=
=
=
=
(1200 2)( ) 50 48 m/min
To keep the flow rate constant, a PLC could control the speed of the conveyor by either computing the flow rate and making changes to a motor or by changing the drive reference speed of the motor. It could also control the analog valve, varying the hopper output according to the required flow rate and speed.
where:
Q W V L
=
=
=
=
the rate of flow
the mass/weight of the solid
the velocity/speed of the moving transporter the length of the weight transducer (load cell)
If English units are used—pounds, feet, and feet/min—then Q will be expressed in lbs/min. Conversely, if metric units are used—kg, meters, and meters/min—then Q will be expressed in kg/min.
FLUID FLOW TRANSDUCERS
To measure fluid flow, you must measure one of two conditions in the process line: pressure differential or fluid motion. The two most common devices for measuring the pressure differential in a process line are Venturi tubes and
orifice plates. One of the most common fluid flow transducers for detecting fluid motion is the turbine flow meter. This transducer transforms flow directly into electrical signals.
Pressure-Based Fluid Flow Meters. Both the Venturi tube and the orifice plate are based on the Bernoulli effect, which relates flow velocity to the pressure differential between two points. These fluid flow meters use pressure transducers, which transform pressure into an electrical signal to determine the pressure differential. The strain gauge and the Bourdon C-tube (see Section 13-5) are the two types of transducers most commonly used in pressure-based flow meters. These transducers use the bridge circuit and LVDT techniques, respectively, to convert measured pressure values into electrical signals. If low pressures are to be measured, a Venturi tube or orifice plate may incorporate a low-pressure transducer, such as a bellows, dia-phragm, or capsule to enhance the pressure reading resolution. Figure 13-28 shows these low-pressure transducers.
Figure 13-29 illustrates a diagram of a Venturi tube, while Figure 13-30 shows an orifice plate flow transducer. The pressure differential ∆P in these devices is equal to the difference in pressures P1 and P2. The value ∆P also relates to the velocity of the fluid through the Bernoulli effect. The velocity at point P2 as a function of ∆P is:
V =k ∆P where:
V
P P P
k
=
= −
=
the fluid velocity a constant
∆ 1 2
Figure 13-28. Low-pressure transducers.
Courtesy of Schaevitz Engineering, Pennsauken, NJ
Figure 13-29. Venturi tube diagram and the pressure and velocity at points P1 and P2.
Figure 13-30. Orifice plate flow transducer.
PressureVelocity
Pipe P1 Pipe
P2
P1
P2
V1
V2
Outlet Cone Inlet
Cone Inlet
Throat
Pressure
P1
P1 P2
P2 Flow
Pipe Outside
Orifice Hole Orifice
Plate
Orifice Plate Differential
Pressure Measurement
The constant k takes into account the density of the fluid, the ratio of pipe to obstruction at cross-sectional points P1 and P2, temperature, and other factors. The equation to obtain the flow rate measurement is:
Q VA Ak P
K P
=
=
=
∆
∆ where:
V A
K k A
=
=
=
the fluid velocity
the cross - sectional area of the pipe
a new constant composed of times the area 2
The flow rate value Q gives us the volume per unit time of the flow (ft/min
× ft2 = ft3/min). Note that the velocity times the area at point 1 (V1A1) is equal to the velocity times the area at point 2 (V2A2).
EXAMPLE 13-10
Illustrate the PLC connections and functions necessary to implement the ratio control computation shown in Figure 13-31.
Figure 13-31. Ratio control computation application.
Mixer
ON/OFF Valve
Product B = 40% Product A Product C = 32% Product A Product C ON/OFF
Valve 0–10 VDC
Differential Pressure Flow Meter (Orifice) –10 to +10 VDC Product B
Product A
ON/OFF Valve
ON/OFF Valve
0–10 VDC
Differential Pressure Flow Meter (Orifice) –10 to +10 VDC
Differential Pressure Flow Meter (Orifice) –10 to +10 VDC
SOLUTION
To implement the ratio control of products B and C at the specified percentage of product A (wild flow), we must read the differential pressures (DP) from the orifice flow meter and control the output of the analog servo valves. Figure 13-32 illustrates this ratio control imple-mentation using flow ratio as the process variable.
The discrete output (120 VAC) is connected to the ON/OFF valve, which allows each of the products to flow. Each DP instrumentation symbol represents the differential pressure measurement from the orifice flow meter. These pressure measurements are input to the analog input modules (–10 to +10 VDC). The flow rate for each product, A, B, and C, is:
Q K P
Q K P
Q K P
A A A
B B B
C C C
=
=
=
∆
∆
∆
Figure 13-32. Ratio control implementation.
Mixer
To 120 VAC Discrete Ouput in PLC
C B
A
DP DP
DP
120 VAC Discrete Output
120 VAC Discrete Output
–10 to +10 Analog Output
–10 to +10 Analog Output
–10 to +10 Analog
Input
–10 to +10 VDC Analog
Input 0–10 VDC
Analog Output
120 VAC Discrete Output
Programmable Controller
∆PB ∆PA ∆PC
where KA, KB, and KC are the given constants. The square root value of the analog input ∆P should be taken after the input count value corresponding to it has been converted to engineering units (through linearization, etc.). As product A flows, the PLC computes the flows of products B and C to maintain the proper ratios between A, B, and C (B = 0.40A and C = 0.32A). The PLC must control the output control valves for products B and C to maintain the proper ratios.
Motion Detection Fluid Flow Meters. The turbine flow meter is one of the most common types of motion detection flow meters. This device is used in applications that measure liquid and gas flows, as well as in applications with very low flow rates. Turbine meters are widely used in petrochemical and pipeline transfers of petroleum flows. Special types of turbine flow meters are also used in liquid oxygen and nitrogen gas-metering applications.
A turbine meter consists of a multibladed rotor, which is suspended in a liquid flow. The fluid flow passing through the blades creates a rotary motion in the turbine. This rotary motion creates a magnetic flux that is sensed by a coil inside the turbine flow meter. The coil changes the flux into a small voltage (as low as 10 to 20 mV) and then amplifies it. This design allows the turbine meter to convert the movement of its blades into output pulses that are proportional to the volume passing through the turbine. The output pulses generally provide information in gallons per minute (gpm). Some turbine meters also provide an analog output proportional to the flow rate being measured. Figure 13-33 illustrates a simple diagram of a turbine flow meter.
Figure 13-33. Turbine flow meter.
EXAMPLE 13-11
A programmable controller system receives an analog signal from a turbine flow meter. The flow rate is given as 60 gpm and the area of the pipe is 2 square inches. Find the velocity of the flow to be displayed in feet per second on a four-digit LED display.
Output Pulses/Voltage
Pipe Flow Pipe
Signal-Conditioning Circuit
SOLUTION
The flow rate of the fluid is described by : Q =VA
where:
Q V
A
=
=
=
the flow rate
the velocity of the flow
the cross - sectional area of the pipe The velocity of the flow is:
V Q
= A
Note that the units given must be converted to obtain the velocity in ft/sec. To convert gallons to cubic feet, we must first convert gallons to cubic meters and then to cubic feet:
1 gal 3.785 10 m
m ft
–3 3
3 3
= ×
= 1 35 31. Therefore:
1 3 785 10 35 31
0 1336
gal 3 ft
ft
3
3
=
(
×)( )
=
. − .
.
The cross-sectional area of 2 square inches is equal to 0.0139 square feet and 60 gpm is equal to 1 gallon per second. So, the velocity in ft/sec is:
V =
=
( )( . ) . .
1 0 1336 0 0139 9 61 ft/sec
Hence, to obtain the velocity of a fluid in a pipe in feet/second when the flow rate is given in gpm and the area is given in square inches, the following equation can be used:
V Q
( A
.
ft/sec)
gpm
(sq in)
=