Flow of Fluids

 Chapter 1 

FLOW OF FLUIDS

INTRODUCTION

• Fluid is a substance such as a gas or a liquid that has no fixed shape and flows easily upon application of external pressure. Flow is defined as the action of moving along in a steady, continuous stream. Thus, fluid flow is a part of fluid mechanics that deals with fluid dynamics and is a motion of gases and liquids. The motion of a fluid is due to unbalanced forces, and this motion continues as long as unbalanced forces are applied.

• For example, if you are pouring a water from a beaker, the velocity of water is very high over the edge, moderately high approaching the edge, and very low at the bottom of the beaker. The unbalanced force is gravity, and the flow continues as long as water is available, and the beaker is tilted.

• Fluid flow has all kinds of aspects such as they can be steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational. These characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. As mentioned earlier, fluid flow can be steady or unsteady and it depends on the fluid’s velocity. In steady fluid flow, the velocity of the fluid is constant at any point whereas in case of unsteady, the fluid’s velocity can differ between any two points. Viscosity is a measure of the thickness of a fluid, and very gloppy fluids such as motor oil or shampoo are called viscous fluids. 

• Both gas and liquid flow can be measured in volumetric or mass flow rates, such as L/sec or kg/sec, respectively. Fluid flow measurements are related by the material's density. The density of a liquid is almost independent whereas for gases, the densities of which depend greatly upon pressure, temperature and to a lesser extent, composition. There are several types of flow meter that works, either by measuring the differential pressure within a constriction, or by measuring static and stagnation pressures to derive the dynamic pressure.

TYPES OF MANOMETERS 

• The term manometer is derived from the ancient Greek words 'mamos', meaning thin or rare, and 'matron' meaning measure. A manometer works on the principle of hydrostatic equilibrium and is used for measuring the pressure (static pressure) exerted by a still liquid or gas. Hydrostatic equilibrium states that the pressure at any point in a fluid at rest is equal, and its value is just the weight of the overlying fluid. The manometer is the simplest instrument used for gauge pressure (low-range pressure) measurements by balancing the pressure against the weight of a column of liquid. The action of all manometers depends on the effect of pressure exerted by a fluid at a depth. Following are the advantages of manometers:

1.  Simple and time proven. 
2. They have high accuracy and sensitivity. 
3. Availability of a wide range of filling fluids of varying specific gravities. 
4. It has reasonable cost.
5. There are suitable for low pressure and low differential pressure applications. 
6. The different types of manometers are discussed below.

Simple U-tube Manometer.

• A manometer is a device to measure pressures. A common simple manometer consists of a U-shaped tube of glass filled with some liquid. In its simplest form, this type of manometer consists of an incompressible fluid like water or mercury. Typically, it is mercury because of its high density.

• Consider a U-shaped tube whose both ends are open to the atmosphere is filled with a liquid. The points A and B are at atmospheric pressure and at same vertical height. In another case, Fig. 1.1 (b), consider that the left arm of U-tube top end is closed and there is a sample of gas in the closed end of the tube. The right side of the tube remains open to the atmosphere. The point A, then, is at atmospheric pressure. The point C is at the pressure of the gas in the closed end of the tube. The point B has a pressure greater than atmospheric pressure due to the weight of the column of liquid of height h. The point C is at the same height as B, so it has the same pressure as point B. Thus, pressure at point C is equal to the pressure of the gas in the closed end of the tube. The pressure of the gas trapped in the closed end of the tube is greater than the atmospheric pressure by the amount of pressure exerted by the column of liquid of height h.

•  Another possible arrangement of the manometer where the top of the left side of the tube is closed and the closed end of the tube contains a sample of gas or it contains a vacuum, Fig. 1.1 (c). The point A is at atmospheric pressure. The point C is at some pressure if it contains gas in the closed end of the tube. Since the point B is at the same height as point A, it is at atmospheric pressure. But the pressure at point B is also the sum of the pressure at point C and the pressure exerted by the weight of the column of liquid of height h in the tube. Thus, it can be concluded that pressure at point C is less than atmospheric pressure by the amount of pressure exerted by the column of liquid of height h. If the closed end of the tube contains a vacuum, then the pressure at point C is zero, and atmospheric pressure is equal to the pressure exerted by the weight of the column of liquid of height h. The U-tube manometer is inexpensive and does not need calibration.

• Pressure is defined as the force per area. The SI unit for pressure is the pascal, which is N/m2 . Another common unit for measuring atmospheric pressure is mm of mercury, whose value is usually about 760 mm. If the closed end of the tube, Fig. 1.1(c), contains a vacuum, the height h is about 760 mm. In many situations, measuring pressures in units of length of the liquid in the manometer is perfectly adequate.

• The pressure measurement in manometer is calculated by considering a cylinder of liquid of height h and area A. The weight of the cylinder is its mass ‘m’ times the acceleration due to gravity ‘g’. This is the force exerted by the cylinder of liquid on whatever is just below it. It is expressed as :  

Differential U-tube Manometer

• A differential manometer is a device that measures the difference in pressure between two places. They can range from simple to complex digital equipment. Standard manometers are used to measure the pressure in a container by comparing it to normal atmospheric pressure. Differential manometers are also used to compare the pressure of two different containers. They are used to know which container has greater pressure and how large the difference between the two is.

• The simplest differential manometer is a U-shaped tube with both ends at the same height. A liquid usually used is water or mercury and it rests at the bottom of the tube. If one end of the tube is in a place with higher air pressure, the pressure will push down the liquid on that side of the tube. By measuring the difference between the heights of liquid, it impossible to calculate the difference in pressure. To calculate the difference in pressure, difference in height is multiplied by the density of the gas and the acceleration due to gravity

There are two types of differential manometer namely.   

1. U-tube differential manometer. 
2. Inverted U-tube differential manometer. There are two types of U-tube differential manometers. 
3. U-tube differential manometer at the same level.
4. U-tube differential manometer at the different level. 

• The first type of manometer has two pipes in parallel positio. This type of manometer is used for measuring the fluid pressure difference between these two pipes arranged at same level. The second type of manometer, is used where two pipes are at different place and are not in parallel condition. This type of manometers is used for measuring the fluid pressure between these two pipes arranged at different levels. Differential manometers have a wide range of uses in different disciplines. One example is that they can be used to measure the flow dynamics of a gas by comparing the pressure at different points in the pipe.

Inverted U-tube Manometer 

• The inverted U-tube differential manometer is reciprocal of U-tube differential manometer at the different level. This type of manometers is used to measure accuracy of small difference if pressure is increased. Inverted U-tube manometer is used for measuring pressure differences in liquids. The space above the liquid in the manometer is filled with air. In order to adjust the level of the liquid in the manometer a tap at the top is provided that admits or expels the air. The pressure at the same level in a continuous body of static fluid is equal.

Micro Manometer 

• A micromanometer is used for the accurate measurement of extremely small pressure differences. The micromanometer is another variation of liquid column manometers based on the principle of inclined tube manometer. The meniscus of the inclined tube is at a reference level as shown in the Fig. 1.5, viewing through a magnifier provided with cross hair line. This is done for the condition, P1 = P2. The adjustment is done by moving the well up and down a micrometer. For the condition when P1 ≠ P2, the shift in the meniscus position is restored to zero by raising or lowering the well as before and the difference between these two readings gives the pressure difference in terms of height.

• Micromanometer is a static fluid pressure difference measuring device. Its dynamics can rarely be ignored. Considering manometric fluid as a free body, the forces acting on it are 

1. The weight distributed over the entire fluid. 
2. The drag force due to its motion and the corresponding tube wall shearing stress. 
3. The force due to differential pressure. 
4. Surface tension force at the two ends.  

Inclined Manometer

• For accurate measurement of small pressure differences by an ordinary U-tube manometer, it is essential that the ratio of density of mercury (ρm) to density of water (ρw) should be close to unity. This is not possible if the working fluid is a gas. A manometric liquid of density very close to that of the working liquid and giving at the same time a well-defined meniscus at the interface is not always possible. For this purpose, an inclined tube manometer is used.

REYNOLDS NUMBER AND ITS SIGNIFICANCE  

• The non-dimensional parameter called Reynolds number was discovered by an Irish engineer and physicist Osborne Reynolds in 1883. He identified the fundamental dimensionless parameter that characterizes the behaviors of flowing fluids known as Reynolds number. It was the ratio that shows the effect of viscosity in a given medium which governs the transition between laminar and turbulent flow. Before this invention it was believed that turbulent flow occurs in pipe of large cross-sectional dimensions and flows at high velocities, whereas laminar flow occurs in slow flows in pipe of relatively small cross-sectional dimensions. The role of viscosity and density in affecting the type of motion is not well-characterized.

• According to Reynolds in the laminar flow the pressure drop is linear in the average velocity of the fluid, whereas in turbulent flow he observed that it was approximately proportional to V1.72, where V is the average velocity. The actual dependence of the pressure drop on the velocity for turbulent flow in circular pipe is more complicated. The roughness of the interior pipe wall in contact with the fluid affects the pressure drop. He proposed that the change in the nature of the flow occurs when a certain combination of the parameters in the flow crosses a threshold. This combination was named after his name as Reynolds number. 

BERNOULLI’S THEOREM AND ITS APPLICATIONS  

Bernoulli’s Theorem.

Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady or streamline flow. This theorem describes relation among the pressure, velocity, and elevation in a moving fluid such as liquid or gas. According to this theorem the compressibility and viscosity (internal friction) are negligible, and the flow is steady, or laminar. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states that ‘the total mechanical energy of the flowing fluid comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid remains constant’. In simple terms Bernoulli's theorem can be described as ‘within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed’.
• Incompressible fluids have to speed-up when they reach a narrow-constricted section in order to maintain a constant volume flow rate. This is why a narrow nozzle on a hose causes water to speed-up. If the water is speeding-up at a constriction means it is gaining kinetic energy. To give kinetic energy is to do work. So, if a portion of fluid is speeding up, something external to that portion of fluid must be doing work it. For example, consider that water flowing along streamlines from left to right, As the outlined volume of water enters the constricted region it speeds up. The force from pressure P1 on water pushes to the right and does positive work. The force from pressure P2 on the fluid pushes to the left and does negative work since it pushes in the opposite direction as the motion of the fluid.

•  The pressure on the wider/slower side P1 has to be larger than the pressure on the narrow/faster side P2. This inverse relationship between the pressure and speed at a point in a fluid is called Bernoulli's principle.

Bernoulli's Equation:

• Bernoulli's equation is a general and mathematical form of Bernoulli's principle that takes into account changes in gravitational potential energy. Bernoulli's equation relates the pressure, speed, and height of any two points (1 and 2) in a steady streamline flowing fluid of density ‘ρ’.

• Bernoulli’s theorem investigates the distribution of pressure in a moving incompressible fluid.

• For the instance consider that throughout the system the diameter of the pipe and the temperature is constant. The represents a channel conveying a fluid from point 1 to point 2. The pump provides energy to cause the flow in upward direction. Assume that one pound of fluid enters the channel at point 1. The pressure at this point is P1 lb/ft2 . If the average velocity of fluid is V1 lb/sec and specific volume of fluid is V1 ft3 /lb. The point 1 is at height h1 above the horizontal bottom plane. The potential energy of a pound of fluid at point 1 is equal to h1 ft.lb. Since fluid is in motion with velocity V1, a pound of fluid will have a kinetic energy equal to V2 1 /2gc ft.lb. This expression is based on average velocity (V) of fluid in the system. In reality the average velocity differs from the mean velocity. The kinetic energy per pound of fluid flowing in channel is given by 

• If there is no gain or loss of energy in the system between point 1 and 2 it follows the principle of conservation energy. But it has been postulated that the energy is added by the pump. This energy is ‘W’ ft.lb/lb of fluid. Some of the energy is converted into heat by friction and dissipated into environment through radiation as system is at constant temperature.

Applications 

• Bernoulli's equation allows us to estimate the flow rate of fluid through a pipe.

• It allows us to measure the change in velocity and pressure experienced by a fluid running from a pipe of some cross-sectional area into a pipe of a different crosssectional area. A fluid will have increased velocity and decreased pressure as it flows from a bigger pipe to a smaller pipe. This relationship is especially important in preventing a malfunction in water pipes through maintaining the stable fluid pressure. If the pressure is too high, the pipe explodes causing damage and other problems

• It can be used to calculate the lift force on an airfoil, if the behaviour of the fluid flow in the vicinity of the foil is known.

• The Pitot tube and static port on an aircraft are used to determine the air speed of the aircraft. Bernoulli's principle is used to calibrate the air speed indicator so that it displays the indicated air speed appropriate to the dynamic pressure. 

• A De Laval nozzle utilizes Bernoulli's principle to create a force by turning pressure energy generated by the combustion of propellants into velocity. 

• The flow speed of a fluid can be measured using a device such as a Venturi meter or an orifice plate, which can be placed into a pipeline to reduce the diameter of the flow. For an incompressible fluid, the reduction in diameter may cause an increase in the fluid flow speed. Bernoulli's principle shows that there must be a decrease in the pressure in the reduced diameter region.

• The maximum possible drain rate for a tank with a hole or tap at the base can be calculated directly from Bernoulli's equation and is found to be proportional to the square root of the height of the fluid in the tank. Viscosity lowers this drain rate. This is reflected in the discharge coefficient, which is a function of the Reynolds number and the shape of the orifice. 

• The Bernoulli grip relies on this principle to create a non-contact adhesive force between a surface and the gripper

ENERGY LOSSES   

• The change in velocity of the fluid in a flow (either in magnitude or direction) induces large scale turbulence due to formation of eddies. So, a portion of energy possessed by the flowing fluid is ultimately dissipated as heat by radiation and is considered to be the loss of energy. Some of the reasons for loss of energy caused by the change in velocity are sudden pipe enlargement, sudden contraction, entrance to a pipe from large vessel, exit from a pipe, obstruction in the flow passage, gradual contraction or enlargement, bends and various pipe fittings etc. These losses of energy are termed as 'minor' losses because the magnitude of these losses is quite small compared to the loss due to friction in long pipes which are distinguished as 'major losses'. The 'minor losses' are confined to a very short length of the passage of the flowing liquid. The analytical expressions representing the loss of energy for above cases are discussed below.

Energy Loss by Sudden Enlargement 

• Consider a pipe of cross-sectional area A1 carrying a liquid of specific weight w. It is connected to another pipe of larger cross-sectional area A2. As there is sudden increase in the cross-sectional area of flow passage the liquid released from smaller pipe is unable to follow the abrupt change in boundary

 

Energy Loss by Sudden Contraction 

• Consider a pipe carrying certain liquid of specific weight w whose cross-sectional area at a certain section reduces abruptly from A1 to A2 as shown in Fig. 1.11. A sudden contraction in geometry of pipe leads to streamlines between section ‘1' and ‘2' curved and the liquid is accelerated. Thus, pressure at the annular face varies in an unknown manner and it cannot be determined. There is no major loss of energy in the region between the section 1 and the accelerating flow in the converging part. 

• As the liquid flows from the wider pipe to narrower pipe, a vena-contract is formed and is followed by further widening of liquid stream to fill up completely the narrower pipe. In between the vena-contract and the wall of the pipe, lot of eddies are formed that accounts for considerable dissipation of energy. In this region, the flow pattern is almost similar to that of sudden enlargement

Energy Loss at Pipe Entrance

• Energy loss at the entrance to the pipe is also called as 'inlet loss'. It occurs, when the liquid enters to the pipe from a large vessel (or tank). The flow pattern is similar to that of sudden contraction. In general, for a sharp-cornered entrance, the loss of head at the entrance is expressed as :

• where, V2 is the mean velocity of flow of liquid in the pipe

Energy Loss at Pipe Exit

• The outlet ends of a pipe carrying liquid may be either left free or connected to a large reservoir. The liquid leaving the pipe possesses some kinetic energy corresponding to the velocity of the flow in the pipe which is ultimately dissipated either in the form of free jet or turbulence in the reservoir depending on the outlet condition in the pipe. The loss may be determined by using Eq. (1.30) with the conditions for which A2 → ∞. So, the loss of head at the exit of the pipe expressed as

• where, V is the mean velocity of flow of liquid in the pipe.

Energy Loss by Obstruction in Flow Passage

• The loss of energy due to flow obstruction in a pipe occurs due to the sudden reduction in the cross-sectional area followed by an abrupt enlargement of the stream beyond the obstruction.

 

 

• Consider a pipe flow (cross-sectional area of the pipe is A) in which an obstruction is placed with maximum cross-sectional area ‘a’. As the flow passage is reduced to (A − a), a vena-contract a is formed beyond which the flow becomes uniform after certain distance from vena-contract. If Ve and V be the velocities at vena-contract and at section where the flow is uniform, then the loss of head due to obstruction can be deduced

FLOW MEASUREMENT DEVICES

• Flow measurement is the quantification of bulk fluid. Volumetric flow rate is measured in "standard cubic centimeters per minute", a unit acceptable for use with SI. In engineering, the volumetric flow rate (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes per unit time; usually represented by the symbol Q (sometimes V̇ ). The SI unit is m3 /s. Flow rate can be measured in a variety of ways. Positivedisplacement flow meters accumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow. Other flow measurement methods rely on forces produced by the flowing stream as it overcomes a known constriction, to indirectly calculate flow. Flow may be measured by measuring the velocity of fluid over a known area.

Orifice Meter

• The orifice meter is made-up of stainless steel, phosper bronze, nickel and monel. An orifice meter provides a simpler and cheaper arrangement for the measurement of flow through a pipe. Orifice is a thin circular plate with a sharp edged concentric circular hole in it. The main part of an orifice flow meter is a stainless-steel orifice plate which is held between flanges of a pipe carrying the fluid whose flow rate is being measured. An orifice plate is fitted between the flanges which are at a certain distance. In order to maintain laminar flow conditions, the pipe carrying the fluid is straight. Openings are provided at two places (a) and (b) for attaching a differential pressure sensor (U-tube manometer, a differential pressure gauge) as shown. The area (A0) of the orifice is much smaller than the cross-sectional area of the pipe. The flow from an upstream is uniform and adjusts itself in such a manner that it contracts until a section downstream the orifice plate is reached at vena contract (b) and then expands to fill the passage of the pipe. The vena-contracts length depends on the roughness of the inner wall of the pipe and sharpness of the orifice plate. One of the pressure tapings is provided at a distance equal to diameter of pipe at upstream to the orifice plate where the flow is almost uniform (a) and the other at a distance of half a diameter of pipe to downstream the orifice plate

Operation:

• In order to know how orifice meter works the details of the fluid movement inside the pipe and orifice plate has to be understood. The fluid having uniform cross-section of flow converges into the orifice plate’s opening in its upstream (left side). When the fluid comes out of the orifice plate’s opening, its cross-section is minimum and uniform for a particular distance and then the cross-section of the fluid starts diverging in the downstream (right side). At the upstream of the orifice, before the converging of the fluid, the pressure of the fluid (P1) is at maximum. As the fluid starts converging and enters the orifice opening its pressure drops. Whereas, when the fluid comes out of the orifice opening, its pressure is minimum (P2) and this minimum pressure remains constant in the minimum cross-sectional area of fluid flow at the downstream. This minimum cross-sectional area of the fluid obtained at downstream from the orifice edge is called vena-contracta. The manometer attached between points (a) and (b) records the pressure difference (∆P = P1 – P2) between these two points which becomes an indication of the flow rate of the fluid through the pipe when calibrated

Applications:

• The concentric orifice plate is used to measure flow rates of pure fluids.

• The eccentric and segmental orifice plates are used to measure flow rates of fluids containing suspended materials such as solids, oil mixed with water and wet steam. 

Advantages: 

• It is very cheap and easy method. 

• It has predictable characteristics and requires less space.

• It can be used to measure flow rates in large pipes.

Limitations: 

• In certain cases it becomes difficult to tap the minimum pressure (P2) due to roughness of the inner wall of the pipe and sharpness of the orifice plate. 

• Pressure recovery at downstream is poor, i.e. overall loss varies from 40% to 90% of the differential pressure. 

• The upstream pipe must be straight to obtain laminar flow. 

• Chances of clogging the orifice when the suspended fluid flows. 

• The orifice plate gets corroded and due to this there may be inaccuracy in determination. 

• The orifice plate has low physical strength. 

• The coefficient of discharge is low. 

Venturi Meter

• Venturi meter is a flow measurement instrument or device used to measure discharge through a pipe. It is based on Bernoulli’s principle.

Construction: 

• A venturimeter is essentially a short pipe, consisting of two conical parts with a short portion of uniform cross-section in between. This short portion has the minimum area and is known as the throat. The two conical portions have the same base diameter, but one is having a shorter length with a larger cone angle while the other is having a larger length with a smaller cone angle. 

Working: 

• The variation in the conical portion at upstream and on the downstream ensures a rapid converging passage and a gradual diverging passage in the direction of flow. This is just to avoid the loss of energy due to separation at the throat. During a flow through the converging part, the velocity increases in the direction of flow according to the principle of continuity, while the pressure decreases according to Bernoulli’s theorem. The velocity reaches its maximum and pressure reaches its minimum at the throat. Subsequently,

• a decrease in the velocity and an increase in the pressure take place in course of flow through the divergent part. Shows that a venturimeter is inserted in an inclined pipeline in a vertical plane to measure the flow rate through the pipe. Let us consider a steady, ideal and one dimensional (along the axis of the venturi meter) flow of fluid. Under this situation, the velocity and pressure at any section will be uniform. 

Pitot Tube

• Pitot tube is a device, invented by Henri Pitot, a French engineer in 18th century, used to measure the fluid flow. The principle of flow measurement by Pitot tube was first used for measuring velocities of water in the river. A right-angled large glass tube was used for the purpose. One end of the tube faces the fluid flow while the other end remains open to the atmosphere,

Working:

• A pitot tube is a simple round cylinder with one end opened with a small hole and the other end is enclosed. The fluid flowing through the pipe enters the Pitot tube and rest there. There is another chamber within the Pitot tube filled with fluid with static pressure. A diaphragm separates both the chambers. The differential pressure is measured between both the pressures that give the dynamic pressure. The difference in level between the liquid in the tube and the free surface becomes the measure of dynamic pressure. The flow rate is calculated from the square root of the pressure. The flow rate depends on the tube design and the location of the static tap. The Pitot-static probe incorporates the static holes in the tube system to eliminate this parameter. 

where, ∆p is the difference between stagnation and static pressures. The factor C takes care of the non-idealities, due to friction, in converting the dynamic head into pressure head and depends, to a large extent, on the geometry of the Pitot tube. The value of C is usually determined from calibration test of the Pitot tube.

Applications:  

• It is widely used to measure the airspeed of aircrafts, speedboat speed and for fluid flow measurement in industrial application. 

• Pitot tubes are mainly used for gas lines. 

• These may be employed where the flowing fluid is not enclosed in a pipe or duct. For example, for measuring the flow of river water, or for measuring air flow in aero plane. 

Advantages:

• Pitot tube is small and do not contain any moving parts. 

• Low permanent pressure loss. 

• Loss of head is negligible by insertion of Pitot tube. 

• It is very cheap as compared to venturi meter, orifice plate and flow nozzle. 

• Ease of installation into an existing system. 

Disadvantages: 

• The differential pressures produced are usually low, say of the order of 250 Pa, and so their sensitivity is low. 

•  Pitot tube requires higher flow velocity in order to produce measurable heads.

• It has small openings which get clogged due to passing solid particles and thus may disrupt normal reading as a result.  

• It requires high fluid velocity, of the order 15 m/s to produce a measurable differential pressure. 

• There is no standardization of pitot tubes. Each Pitot tube is required to be calibrated for each installation. 

Rota Meter

• A rotameter is a device that measures the volumetric flow rate of fluid in a closed tube. These are the most widely used type of variable-area flow meter. It measures flow rate by allowing the cross-sectional area the fluid travels through to vary, causing a measurable effect.

Construction:

• A rotameter consists of a tapered tube, typically made of glass with a 'float' (made either of anodized aluminum, ceramic or plastic), inside that is pushed up by the drag force of the flow and pulled down by gravity. The drag force for a given fluid and float cross-section is a function of square of flow speed. A higher volumetric flow rate through a given area increases flow speed and drag force, so the float is pushed upwards. However, as the inside of the rota meter is cone shaped, the area around the float through which the fluid flows increases, the flow speed and drag force decrease until there is mechanical equilibrium with the float's weight.

• Floats are made in many different shapes, with spheres and ellipsoids being the most common. The float may be diagonally grooved and partially colored so that it rotates axially as the fluid passes. This shows if the float is stuck since it will only rotate if it is free. Readings are usually taken at the top of the widest part of the float, the center for an ellipsoid, or the top for a cylinder. The float must not float in the fluid, and it has to have a higher density than the fluid; otherwise, it will float to the top even if there is no flow. The mechanical nature of the device does not require any electrical power. If the tube is made of metal, the float position is transferred to an external indicator via a magnetic coupling. The measurement can be made remotely from the process or used for automatic control. 

 

Working:

• In these devices, the falling and rising action of a float in a tapered tube provides a measure of flow rate. Rota meters are also known as gravity-type flow meters because they are based on the opposition between the downward force of gravity and the upward force of the flowing fluid. When the flow is constant, the float stays in one position that can be related to the volumetric flow rate. That position is indicated on a graduated scale. In order to keep the full force of gravity in effect, this dynamic balancing act requires a vertical measuring tube.

Applications: 

• The rotameter is used in process industries to measure fluid flow rates. 

• It is used for monitoring gas and water flow in plants or labs.

• It is used for monitoring filtration loading. 

Advantages: 

• It has good accuracy for low and medium flow rates. 

• The pressure loss is nearly constant and small. 

• It can be used for corrosive fluids. 

• It requires no external power or fuel; it uses only the inherent properties of the fluid, along with gravity. 

• A rotameter is a relatively simple device that can be mass manufactured out of cheap materials, allowing for its widespread use and thus cost is low. 

• Since the area of the flow passage increases as the float moves-up the tube, the scale is approximately linear. 

•  Clear glass can be used as this is highly resistant to thermal shock and chemical action. 

Disadvantages: 

• It is not suitable for opaque fluids as float may not be visible through them. 

• Glass tube may be subjected to breakage. 

• As this device is based on gravitational force it requires to be installed in vertical position only.

•  Calibration scale on rote meter need to be accurate for a given substance at a given temperature. 

• A separate Rota meter is needed for fluids with different densities and viscosities or are supplied with multiple scales on the same Rota meter. 

• Readout uncertainty gets worse near the bottom of the scale. 

• Oscillations of the float and parallax may increase the uncertainty of the measurement. 

• A transducer may be required for electronically measuring the position of the float. 

• Rota meters are not easily adapted for reading automatically. 

• Rota meters are not generally manufactured in sizes greater than 6 inches (150 mm).