# Flow measurements info notes # Static Properties, not in motion

Static pressure, the pressure exerted by fluids at rest.

# Density

Density is a measurement of the proximity of molecules that make up a substance. Density is Mass per Unit of Volume ( r = m / V ), where: r = Density, m = Mass, and V = Volume.

# Effects of Temperature and Pressure on Density

Heating causes a substance to expand, increasing its volume, and decreasing its density. Cooling causes a substance to contract, decreasing its volume, and increasing its density. More pressure causes a substance to compress, decreasing its volume, and increasing its density. Less pressure causes a substance to expand, increasing its volume, and decreasing its density.

# Specific Gravity

Specific Gravity is the ratio comparing the density of a fluid to the density of water or air while at standard conditions.

Specific Gravity = Density of a liquid / Density of water.

Specific Gravity = Density of a liquid / Density of air.

The Specific Gravity of Liquids and Gases will decrease as temperature increases.

# Dynamic Properties, in motion flowing

Dynamic pressure, the pressure above static pressure caused by movement of fluids.

# Flow

In laminar flow, the fluid particles move along parallel paths. If laminar flow could be observed, it would appear as several streams of liquid flowing smoothly alongside each other.

Turbulent flow is agitated and disturbed. Turbulent flow appears to have small, high frequency fluctuations that travel in all directions forming eddies.

Transitional flow exhibits characteristics of both laminar and turbulent patterns. In some cases, transitional flow will oscillate between laminar and turbulent flow.

# Viscosity

Viscosity is the property that determines how freely fluids flow. Viscosity can be further described as the property of a fluid that contributes to laminar or turbulent flow characteristics. If the molecules slide easily over one another, the substance has a relatively low viscosity. A substance with a higher viscosity has a higher resistance to flow.

# Effect of Temperature on Viscosity

Small changes in temperature may produce significant changes in a fluid's viscosity. As the Temperature of a fluid decreases, its viscosity will increase.

Temperature of a fluid increases, its viscosity will decrease.

# Reynolds Number

Flow is often measured in terms of velocity. Therefore, when different portions of the flow are moving at different velocities, measurement accuracy will be affected. The flow profile depends on a combination of factors, including the forces that act to keep flow moving at a constant rate. The relationship between these forces is expressed by the Reynolds number ( RD ). It is a ratio of internal to viscous forces specific to flow conditions where RD = Inertial forces / Viscous forces.

When the Reynolds number is less than 2000, flow is in the laminar region. When the Reynolds number is greater than 4000, flow is considered to be in the turbulent region. When the Reynolds number is in the range of 2000 to 4000, flow is transitional. Viscosity is the factor which most affects the value of the Reynolds number.

# Flow Rate

The measurement unit to express the rate of flow actually refers to the velocity of the flow, or how rapidly the substance moves. A flow rate is a measure of the distance a particle of a substance moves in a given period of time. Feet per second is a unit commonly used to measure flow rate.

# Volumetric Flow Rate

The method of measurement used to indicate the volume of fluid that passes a point over a period of time is volumetric flow rate. Volumetric flow rate is usually expressed in gallons per minute (GPM) or cubic feet per second.

# Mass Flow Rate

Mass flow rate determines the amount of mass that passes a specific point over a period of time. Mass flow rate applications determine the weight or mass of the substance flowing through the system.

# 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.

# 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 makes some 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 totalized 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.

# Orifice Plate

The most common and the simplest differential producer is the orifice plate. An orifice plate is usually composed of stainless steel. An opening of a predetermined size and shape is machined into the plate according to strict tolerances. Then, the orifice plate is inserted perpendicular to the process flow. This abruptly reduces the stream size, creating a head-producing constriction. Differential pressure is then measured at pressure taps installed upstream and downstream from the orifice plate.

The most common type of orifice plate is the concentric bore where the hole will be in the center of the pipe. An eccentric bore plate is used to minimize measurement inaccuracies that can be caused by solids settling out of the liquid. The eccentric bore is positioned so that the bottom of the hole is even with the inside wall of the pipe.

# Venturi Tubes

The venturi tube places a constriction in the flow path that acts on the same principle as that of the orifice plate. In basic forms, the venturi tube consists of a converging conical inlet, a cylindrical throat, and a diverging recovery cone. Venturi tubes are better suited for the measurement of dirty fluids and slurries which would tend to build up in front of, or clog an orifice plate.

# Flow Nozzles

Flow nozzles are a restriction consisting of an elliptical contoured inlet and a cylindrical throat section. Flow nozzles are well suited for measurement of steam flow and other high velocity fluid flows where erosion may be a problem.

# Elbow - Tap Flowmeters

Elbow-tap flowmeters operate on the principle that when a fluid moves around a curved path, the acceleration of the fluid around the curved path creates a centrifugal force. The centrifugal force results in a higher pressure on the outside of the elbow than on the inside of the elbow. A major advantage is the ease with which they can be installed, however they are less accurate than other head-type measurement devices.

# Pitot Tubes

Consists of two pressure taps in a flow stream. The low pressure tap is perpendicular to the flow path and measures the static head. The high pressure tap is inserted into the flow stream and faces directly into the flow path. By measuring the differential pressure created by the Pitot tube, flow rate can be calculated. Pitot tubes causes negligible pressure loss in the flowing stream, however they are difficult to position properly in the flow stream and are subject to plugging in slurry applications.

# 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.

# 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.

# 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.

# DC Magnetic Flowmeters

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

# 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.

# 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.

# 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.

# 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 flowstream. Thus, the sensor may be clamped onto the pipe or may be mounted in a section of pipe which is installed in the system.

# 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 flowpath 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.

# 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.

# 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.

# 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.

# 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.

# 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.

# 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.

# 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.

# Shedders

Vortex shedders are a type of oscillatory flowmeter. Such flowmeters employ a physical phenomena that cause discrete changes in some parameter that is a function of the flow through the flowmeter.

# Theory of Operation

Vortex shedding can occur whenever a blunt or flat-faced body, called a bluff body, is positioned in a flowing stream of gas or liquid. As fluid passes a bluff body at low velocity, the flow is able to follow the irregular contour. However, as the velocity increases, the fluid tends to separate into layers and swirl around the body to form vortices downstream of it. When a vortex on one side of the bluff body breaks away from the body, it is followed by a new one on the opposite side of the body. That in turn also breaks away, followed by a new vortex on the opposite side. This alternating pattern of vortices is called a Von Karman vortex trail. The alternate shedding of vortices is the basis of meter operation. It is this increase and decrease of pressure across the bluff body which is measured to determine a frequency of vortex formation. The frequency of the vortex generation is directly proportional to the fluid velocity.

# Design

Vortex shedding flowmeters are generally comprised of three basic parts: a shedder, or bluff body, which generates the vortices; a sensor to sense the frequency of the vortices and produce a signal that can be measured; and, a transmitter to amplify and condition the signal.

# Vortex Precession Flowmeter

This type of meter also operates by detecting vortices. However, in this device, the fluid is forced into a swirl condition by swirl-producing vanes, or swirl blades. The center of the vortex becomes displaced from the meter centerline and follows a helical path (precession) as it moves downstream through an enlargement. This precession causes fluctuations in fluid pressure and velocity. A sensor placed downstream from the swirl blades detects and measures the frequency of the precession. This frequency is linearly proportional to flow rate.

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