Hai,

your question is very good indeed but i like to clarify your doubt, in flow transmitter the thing u generally observed is that square root extractor, that simply means the property of orifice meter ie Q√DELTAP ie differential pressure generated in up-stream-down stream.As it is the basic equation of orifice, so to maintain the property the flow tx are designed like this,and not like linear.Now a days the sqare root extractor facility comes in built with PLC,DCS.

Hope u get u r answer,

sanchayan.

its simple...

the flow is measured by measuring the DP (differential pressure) across a restriction (e.g. orifice) in the process fluid. This DP value is used for correlating the flow rate of the fluid. when you look at the flow measuring equation, you will find that the flow rate is a function of the square root of the DP measured. So, a square root function in the flow transmitter is incorporated to convert the DP value into a flow rate value.

Hope this clears your doubt.

I should have the equation as well with me. Let me check my old books.

Ref Bernoulis Theorm , or Crane TP 410 You Will Understand the reason Why Square Root Term is Getting introduced

Regards

Jose John

One only needs to set square root for a differential pressure transmitter across an orifice plate, as the pressure difference is proportional to the square root of the flowrate.

Orifice plate flowmeters are just so, so, well, passé; so "1973". There are many other ways to measure flow, and several of these do not need the square root function.

Hi Guest,

http://www.pc-education.mcmaster.ca/instrumentation/flow.htm

This is a brilliant site!

The Square Root Law is to show the 'volume' of the flow, as well as showing the speed of what is presumed to be a 'liquid' whose viscosity and density are constant.

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The answer to your question on the Square Law is below:

Differential Pressure

The rate of flow using a head flowmeter device is determined by measuring the pressure drop across a constriction. Differential pressure is measured and flow rate is inferred from the measured difference in the two related pressures.

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Bernoulli's Law

Head-flow type flow measurement is based on the principle that energy cannot be created or destroyed. Consequently, in a pipe, with fluid flowing, the same volume of fluid will pass by two different points over the same period of time. However, if the fluid flow passes through a constriction, the flow velocity must increase if the flow rate is to remain constant,. Therefore, to maintain the flow rate between the two different points the total energy of the fluid must also remain constant.

All head-type differential pressure flowmeters operate on the conservation of energy principle. The primary sensing element creates a differential pressure by constricting the fluid flow, while a secondary element measures this differential pressure. The relationship between differential pressure and flow is:

Q = CA times the square root of ( 2 gh )

where:

Q = flow

C = orifice coefficients

A= cross-sectional area of the restriction

g = gravitational constant

h = head or differential pressure

This square root or "square law" relationship of flow to differential pressure, can be a disadvantages of head-type flowmeters apparent.

Measurement of flows of less than 30 percent of maximum may be less accurate than a measurement at a higher percent of maximum flow.

The square root relationship also makes integrating or totalizing of flows cumbersome and the accuracy of tantalized flow somewhat questionable. In addition, this relationship represents a nonlinear effect on loop gain in flow control systems, requiring controller readjustment at different rates of flow. The nonlinear effect results in loss of accuracy below 50 percent of the measurement span.

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Other types of Flow Meter:

Mass

In some industrial processes, accurate measurement of mass flow is required. Mass is defined as a measure of the quantity of matter in a body. Mass is one of the three fundamental quantities, the others being length and time, upon which all physical measurements are based. Often mass is thought of as weight, but these quantities are dissimilar. Weight is the measure of the effect of earth's gravity on mass and varies over the earth's surface.

Angular Momentum Mass Flowmeter

The angular momentum mass flowmeter is a true mass flowmeter since the reaction of the primary element is proportional to the momentum of the flow stream. In this type of device fluid passes through an impeller and a turbine mounted in series in a pipeline. The impeller is driven at a constant speed by a small motor. As it is rotated, it causes the fluid entering the impeller to take on its rotational velocity. The fluid then enters a turbine that is restrained by a calibrated spring and does not rotate. The torque produced by the turbine on the calibrated spring is directly proportional to the mass flow.

Coriolis Flowmeters

The Coriolis flowmeter is a true mass flowmeter which operates on the physical principle of the effects of the earth's rotation on a mass. This effect is referred to as the Coriolis acceleration and produces a Coriolis force. Since torque is equal to mass multiplied by acceleration, a measurement of the Coriolis force provides the means for a direct determination of mass flow.

One type of Coriolis mass flowmeter consists of an impeller with radial vanes. The meter is positioned so the vanes are in line with the flow. The impeller, powered by a small motor turns at a constant rate. The vanes direct the flow in a direction that is radial and perpendicular to the axis of rotation., this results in a Coriolis acceleration which then exerts a force on the vanes. Force-sensing devices measure the torque produced, and, since the amount of torque is directly proportional to the mass flow rate, the value can be used to calculate the rate directly.

The vibrating U-tube is another type of mass flowmeter that uses the principle of Coriolis acceleration of a fluid. The U-tube offers no obstruction to the flow-path allowing it to measure liquids with varying physical properties. In addition, this type of flowmeter may be used with liquids containing solids. The flowmeter consists of a vibrating U-tube in which the Coriolis acceleration is created and measured. An oscillator vibrates the tube rapidly along the axis formed between its open ends. Because of this alternation, the fluid in one arm of the tube flows away from the axis of rotation while in the other half, the same amount of fluid flows towards the axis of rotation. These opposing Coriolis accelerations result in forces in the opposite directions, which produce a twisting motion in the tube which is directly proportional to the mass flow through the U-tube, is detected by a sensing device.

Hydraulic Wheatstone Bridges

The hydraulic Wheatstone bridge mass flowmeter is a true mass flowmeter which uses differential pressure to measure the mass flow. Four identical orifice plates are placed in a Wheatstone bridge arrangement. A portion of the flow is pumped at a constant rate from one segment of the fluid loop to another segment of the loop. A Differential pressure transmitter is then used to sense the flow signal.

Positive Displacement Flowmeters

In many applications, positive displacement flowmeters provide significant advantages over meters of other classes. They are accurate, precise, have a wide flow range and are ideal for measuring low rates of flow. In addition, their operation requires no external power supply and they usually require only simple maintenance. Positive displacement flowmeters operate by trapping a known quantity of fluid, and transferring the fluid from the inlet to the outlet connections. Then the number of trapped volumes that pass through the meter is counted to measure the flow.

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Nutating Disc Flowmeter

The meter consists of a housing containing a disc which is allowed to wobble, or nutate. As fluid enters the inlet port of the meter, its movement in the chamber causes the disc to turn or nutate. As the disc turns, it transfers a fixed quantity of fluid from the inlet to the outlet.

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Helical Gear Positive Displacement Flowmeter

In this type of positive displacement flowmeter, two radically-pitched helical gears are used to continually trap liquid as it passes through the flowmeter. A sensing system, typically magnetic or optical, senses a pulse each time a portion of a revolution occurs. Flow through the flowmeter is proportional to the rotational speed of the gears.

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Oscillating Piston Positive Displacement Flowmeters

When a quantity of fluid enters the chamber it causes a piston to rotate on its shaft. As it does so, a specific volume of fluid is moved through the meter and discharged at the outlet port. Each revolution of the piston corresponds to the movement of a fixed volume of fluid through the meter. A sensing system, typically magnetic or optical, senses a pulse each time a portion of a revolution occurs.

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Rotary Vane Flowmeters

As fluid enters the meter, vanes are moved causing the rotor to turn. The vanes are spring loaded and able to slide freely in the rotor body as it turns, When the fluid enters the inlet port, the vanes extend against the housing wall to enclose the measuring chamber, they retract at the outlet to discharge the fluid into the system. Each complete revolution of the rotor moves several fixed volumes of fluid through the meter from inlet to outlet.

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Lobed Impeller and Oval Gear Flowmeters

Two lobed impellers (rotors) are mounted on parallel shafts and are geared-synchronized to keep them correctly positioned in relation to each other. These lobes rotate in opposite directions, so as fluid enters the meter and causes the impellers to rotate, a measuring chamber is formed.

The oval gear flowmeter is a variation of the lobed impeller flowmeter. The lobed impellers are replaced by a pair of meshed oval gears.

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Axial Turbine Flowmeters

In current-type meters, a discrete volume of fluid is not actually captured and transferred from inlet to outlet to measure flow rate as it is in a positive displacement meter. Rather, the total quantity of flow is inferred from the reaction of the turbine caused by the fluid flow.

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Rotameters

The rotameter consists of a tapered glass tube which is incorporated into the piping system. The tube is positioned so its greatest diameter is uppermost and contains a float which moves up and down freely as the flow within the tube changes. Since the upward and downward forces on the float are in equilibrium, the float assumes a definite position at a given flow rate.

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Magnetic Flowmeters

Magnetic flowmeters are widely used to measure the flow rate of conductive liquids in process applications. In general, magnetic flowmeters are accurate, reliable, measurement devices that do not intrude into the system.
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Principle of Operation

Magnetic flowmeters operate on the principle of Faraday's Law of Electromagnetic Induction, an electrical voltage is induced in a conductor that is moving through a magnetic field and at right angles to the field. The faster the conductor moves through the magnetic field, the greater the voltage induced in the conductor.
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AC Magnetic Flowmeters

Alternating current (AC) magnetic flowmeters excite the electromagnetic field with AC current. Noise may be produced within the meter or within the process. The zero must be adjusted when the flowmeter is full of process fluid at zero flow. Sensitivity of electrodes may be reduced if the electrodes become coated with a non-conductive material.
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DC Magnetic Flowmeters

Direct current (DC) magnetic flowmeters excite the electro-magnetic field with a DC current. DC magnetic flowmeters are not subject to inaccuracies due to the coating of electrodes.
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Thermal Flowmeters

In a thermal flowmeter, flow rate is measured either by monitoring the cooling action of the flow on a heated element placed in the flow or by the transfer of heat energy between two points along the flow path.
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Hot Wire Anemometers

Hot wire anemometers have probes inserted into the process flow. These probes are usually connected in a typical bridge circuit. One of two probes is heated to a specific temperature. The second probe measures the temperature of the fluid. As the flow increases, it causes a heat loss in the heated probe. Consequently, more current is required to maintain the probe at the correct temperature. The increase in current flow reflects the energy necessary to compensate for the heat loss from the probe that was caused by the changing fluid flow. This change in current flow can be measured and used to calculate mass flow rate.
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Calorimetric Flowmeters

Calorimetric flowmeters work on the principle of heat transfer by the flow of fluid. Typically, calorimetric flowmeters are comprised of elements arranged consecutively along the direction of the flow. A heating element is placed in the flow. A sensor is positioned to measure the temperature upstream of the device; a second measuring device reads the temperature of the flow downstream from the heater. The rate of flow is determined by the difference in the two temperatures.
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Ultrasonic Flowmeters

Ultrasonic flow instruments measure the velocity of sound as it passes through the fluid flowing in the pipe. Some designs allow measurements to be made external to the pipe, while others require that the sensor be in contact with the flow-stream. Thus, the sensor may be clamped onto the pipe or may be mounted in a section of pipe which is installed in the system.

I hope this helps.

Hi Guest,

I meant to included this is my previous post but forgot to, sorry.

http://www.flowmeters.co.uk/flow-meter-flow-measurement-bibliography-definition-of-terms/

The Square Root Law applies to most types of differential pressure devices, orifice plates, pitot tubes, etc.

Where the flow is the square root of the differential pressure.

But when using a 'Head Flow Meter' there may not be a need to use this SR/Law.

If the volume and/or flow, and/or density, and/or viscosity are known to be constant, or there is enough liquid by volume to supply the ongoing processes the 'Head' was designed for, then the SR/Law may not be used as part of the flow measure.

A linear flow measure/judgement can be used as an alternative.

Hi B-B,

I've given a GA for this, as it provides an excellent comparison of apparatus and taken together with the web address is a good reference to understanding the principles of flow measurement.

Well done Sir!

Best wishes,

Massey.

AH!

This is proof of the worth of a engineering degree.

Only engineers with a degree are able to understand this concept. Try explaining this to a arts major or a mechanic or even a doctor.

Carry on all you students of engneering!!

Hi, I think engineers are definitely needed and I encourage students to get educated to become one(my son is working in that direction) but to say that "Only engineers with a degree are able to understand this concept" in my opinion that statement is debatable..... Thank you

Your right.

I was being sarcastic. Doctors ofter think they have the lock on knowledge.

It's simple. Square root of DP is flow. that's why.

Flow is proportional to square root of flow thats why DP transmitter uses square root extractor so

Flow = K Sqrt (DP generated from DP Transmitter)

K can be calculated from Orifice (Flow Element) data ,then it gives true flow .

Yokogawa EJA 910 and Rosemount 3095 is true flow transmitter.

Pt Sushil