Guided by Prof. Pratik Patel NamePen Meet mistry jigar dholariya Kush naik

Principles of Fluid Flow in Pipes In laminar flow, the fluid travels as parallel layers (known as streamlines) that do not mix as they move in the direction of the flow. If the flow is turbulent, the fluid does not travel in parallel layers, but moves in a haphazard manner with only the average motion of the fluid being parallel to the axis of the pipe. If the flow is transitional, then both types may be present at different points along the pipeline or the flow may switch between the two. In 1883, Osborne Reynolds performed a classic set of experiments that showed that the flow characteristic can be predicted using a dimensionless number, now known as the Reynolds number.

Principles of Fluid Flow in Pipes The Reynolds number Re is the ratio of the inertia forces in the flow to the viscous forces in the flow and can be calculated using: If Re < 2000, the flow will be laminar. If Re > 4000, the flow will be turbulent. If 2000<Re<4000, the flow is transitional The Reynolds number is a good guide to the type of flow

Principles of Fluid Flow in Pipes

The Bernoulli equation defines the relationship between fluid velocity (v), fluid pressure (p), and height (h) above some fixed point for a fluid flowing through a pipe of varying cross- section, and is the starting point for understanding the principle of the differential pressure flowmeter. Bernoulli’s equation states that:

Bernoulli’s equation can be used to measure flow rate. Consider the pipe section shown in figure below. Since the pipe is horizontal, h 1 = h 2, and the equation reduces to:

Principles of Fluid Flow in Pipes The conservation of mass principle requires that:

Differential Pressure Flowmeters The Orifice Plate The orifice plate is the simplest and cheapest. It is simply a plate with a hole of specified size and position cut in it, which can then clamped between flanges in a pipeline The increase that occurs in the velocity of a fluid as it passes through the hole in the plate results in a pressure drop being developed across the plate. After passing through this restriction, the fluid flow jet continues to contract until a minimum diameter known as the vena contracta is reached.

The Orifice Plate

The orifice plate is the simplest and cheapest. The increase that occurs in the velocity of a fluid as it passes through the hole in the plate results in a pressure drop being developed across the plate. After passing through this restriction, the fluid flow jet continues to contract until a minimum diameter known as the vena contracta is reached. The equation to calculate the flow must be modified to

The Venturi Tube The classical or Herschel Venturi tube is the oldest type of differential pressure flowmeter (1887). The restriction is introduced into the flow in a more gradual way The resulting flow through a Venturi tube is closer to that predicted in theory so the discharge coefficient C is much nearer unity (0.95). The pressure loss caused by the Venturi tube is lower, but the differential pressure is also lower than for an orifice plate of the same diameter ratio.

The smooth design of the Venturi tube means that it is less sensitive to erosion than the orifice plate, and thus more suitable for use with dirty gases or liquids. The Venturi tube is also less sensitive to upstream disturbances, and therefore needs shorter lengths of straight pipework upstream of the meter than the equivalent orifice plate or nozzle. Like the orifice plate and nozzle, the design, installation, and use of the Venturi tube is covered by a number of international standards. The disadvantages of the Venturi tube flowmeter are its size and cost. The Venturi Tube

The Nozzle The nozzle combines some of the best features of the orifice plate and Venturi tube. It is compact and yet, because of its curved inlet, has a discharge coefficient close to unity. There are a number of designs of nozzle, but one of the most commonly used in Europe is the ISA-1932 nozzle, while in the U.S., the ASME long radius nozzle is more popular. Both of these nozzles are covered by international standards.

Other Differential Pressure Flowmeters There are many other types of differential pressure flowmeter, but they are not very common the segmental wedge, V-cone, elbow, and Dall tube. Each of these has advantages over the orifice plate, Venturi tube, and nozzle for specific applications. For example, the segmental wedge can be used with flows having a low Reynolds number, Dall tube has a lower permanent pressure loss than a Venturi tube. However, none of these instruments are yet covered by international standards and, thus, calibration is needed to determine their accuracy.

Choosing which flowmeter is best for a particular application can be very difficult. The main factors that influence this choice are the required performance, the properties of the fluid to be metered, the installation requirements, the environment in which the instrument is to be used, and, of course, cost. There are two standards that can be used to help select a flowmeter: BS 1042: Section 1.4, which is a guide to the use of the standard differential pressure flowmeters BS 7405, which is concerned with the wider principles of flowmeter selection

Variable Area Flowmeters The term variable area flowmeters refers to those meters in which the minimum cross-sectional area available to the flow through the meter varies with the flow rate. Meters of this type include the rotameter and the movable vane meter used in pipe flows, and the weir or flume used in open-channel flows. The measure of the flow rate is a geometrical quantity such as the height of a bob in the rotameter, the angle of the vane, or the change in height of the free surface of the liquid flowing over the weir or through the flume.

Rotameter Rotameter consists of a conical transparent vertical glass tube containing a “bob”. The flow rate is proportional to the height of the bob. The rotameter is characterized by: Simple and robust construction High reliability Low pressure drop

Rotameter Applicable to a wide variety of gases and liquids Flow range 0.04 L/h to 150 m3/h for water Flow range 0.5 L/h to 3000 m3/h for air Uncertainty 0.4% to 4% of maximum flow Insensitivity to nonuniformity in the inflow (no upstream straight piping needed) Typical maximum temperature 400°C Typical maximum pressure 4 MPa (40 bar) Low investment cost Low installation cost

Weir

Positive Displacement Flowmeters A positive displacement flowmeter, commonly called a PD meter, measures the volume flow rate of a continuous flow stream by momentarily entrapping a segment of the fluid into a chamber of known volume and releasing that fluid back into the flow stream on the discharge side of the meter. By monitoring the number of entrapments for a known period of time or number of entrapments per unit time, the total volume of flow or the flow rate of the stream can be ascertained. The total volume and the flow rate can then be displayed locally or transmitted to a remote monitoring station.

Sliding-vane type PD meter. Tri-Rotor Type PD Meter Birotor PD Meter Piston Type PD Meter Oval Gear PD Meter

Advantages PD Meters High-quality, high accuracy, a wide range, and are very reliable, insensitive to inlet flow profile distortions, low pressure drop across the meter. Until the introduction of electronic correctors and flow controls on other types of meters, PD meters were most widely used in batch loading and dispensing applications. All mechanical units can be installed in remote locations.

Disadvantages PD Meters bulky, especially in the larger sizes. the fluid must be clean for measurement accuracy and longevity of themeter. More accurate PD meters are quite expensive. Have high inertia of the moving parts; a sudden change in the flow rate can damage the meter. Only for limited ranges of pressure and temperature Most PD meters require a good maintenance schedule and are high repair and maintenance meters. Recurring costs in maintaining a positive displacement flowmeter can be a significant factor in overall flowmeter cost.

Summary For pipe flows, variable area flowmeters are suitable for low flow rates of gases or liquids at moderate temperatures and pressures. Advantage rugged construction, high reliability, low pressure drop, easy installation, and low cost. Disadvantages measurement uncertainty of 1% or more, limited range (10:1), slow response, and restrictions on the meter orientation. Variable area flowmeters in open-channel flows have applications for flow measurements in waste water plants, waterworks, rivers and streams, irrigation, and drainage canals.

Reference krohne.com/en/products/flow-measurement/variable- area-flowmeters