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FLOW measurements

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**INTRODUCTION & DEFINATIONS**

The measurement of flow is important in many industrial processes where the flow rate of liquids or gases is required. The unit for flow rate is cubic meters per second (m3/s) for liquids and kilograms per second (Kg/s) for gaseous fluids. The unit for total flow quantity is m3. m3 = 1000 liter liter = 1000 cm3 m3= 106 cm3

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**DIRECT WEIGHTING OR VOLUMATIC TECHNIQUE**

The time necessary to collect a quantity of liquid in a tank is measured. Accurate measure is then made for the collected mass or volume. The flow rate may be determined by using Eqs. 6.1., and 6.2. Q’ = Q/∆t Eq. 6.1 m’ = m/∆t Eq. 6.2

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Where Q, and m are the collected volume (quantity), and mass respectively. Δt is the time elapsed in collecting the specified quantity. This technique is employed only in calibration of flow meters and may be taken as a standard calibration technique.

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**POSITIVE DISPLACEMENT METERS (MECHANICAL METERS)**

In mechanical meters, the sensing element, which is situated in the pipeline or channel, is displaced by the fluid flowing past it.

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**DEFLECTION VANE FLOW METER**

The deflecting-vane flow meter is normally used for measuring liquid flow rate in open channels or for measuring the velocity of air in ventilating ducts. The meter consists of a pivoted plate or vane suspended in the liquid flow stream as shown in Fig.6.1 In the position shown, the vane is in equilibrium with the flow stream, i.e.

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**Fig. 6.1 Deflection van flow meter**

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The force exerted on the vane by the flowing liquid is being resisted either by the mass of the vane itself or by a suitable spring located on the pivot. The position of the vane is a measure of the rate of flow. The movement of the vane is indicated on a scale, which may be calibrated in units of flow rate, e.g. cubic meters per second (m3/s). The main disadvantages with this device are:- a)It restricts the flow rate. B)It needs to recalibrated for fluids of differing densities

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**ROTATING VANE FLOW METER**

The problem of restriction to flow caused by the deflecting vane may be overcome by making the vane rotate. In the five-blade rotating vane shown in Fig.6.2., the density of fluid is of no importance. The rotating spindle may be connected to a mechanical or electrical speed-measuring device, known as tachometer, which is calibrated in units of volume per unit time, i.e. m3/s.

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**Fig. 6.2. Rotary vane flow meter**

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If the spindle is connected to a counter instead of a tachometer, then the total flow in m3 is determined. The rotating vane illustrated is used in small bores, typically up to 50 mm diameter

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HELICAL TURBINE METER The helical-turbine meter takes the form of a propeller or turbine in which the liquid is made to flow past the turbine blades as shown in Fig. 6.3.

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**Fig. 6.3 Helical turbine meter**

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The rotor is connected via a worm gear and wheel to a mechanical or electrical counter or a tachometer or both, i.e. the meter may be used to measure flow rate and total flow. This type of meter is generally used in larger systems and requires periodic inspection and cleaning of the working parts

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**DRAG EFFECT TECHNIQUE ROTAMETER (VARIABLE AREA METER)**

The fluid enters to the bottom of the tapered vertical tube, and causes the float to move upward. As the float moves upward the annular area between the float, and the tube, increases. This results in decreasing the flow velocity and the drag force. The float will rise to a point such that the weight of the float is just balanced by flow (drag), and the buoyancy forces. If the flow is increased, the float will rise to a new equilibrium position, and if the velocity is reduced the float will fall. The position of the float being a measure of the rate of flow of the fluid. The tube, which may be manufactured from glass or plastics, is graduated in units of flow rate.

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This meter is simple and cheap, and its maintenance is very simple. One of the advantages of this meter is that it can measure very low flow rates. Its main disadvantage is that the tube needs to be recalibrated for fluids of differing densities.

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Fig.6.4 Rotameter

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**FLOW OBSTRACTION METHOD (DIFFERENTIAL PRESSURE METHOD**

An obstruction to the fluid flow is introduced, and the resulting head-loss (Differential pressure) is taken as an indication of the flow rate. Consider the one dimensional flow system shown in Fig. 6.5, The continuity equation for this situation is Eq.6.3

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**Fig. 6.5 General one dimensional system**

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Where the v1, and v2 are the fluid velocity at the inlet and the outlet section respectively. The A1, and A2 are the cross section areas of the duct inlet and outlet respectively. Applying Bernoulli equation Eq. 6.4 Eq. 6.5 Eq. 6. 6 Eq. 6.7

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**Where Δh is the differential head **

Velocity approach factor = E = Eq. 6.8 Substitute in equation 6.7 by eq.6.8 Eq. 6.9 Friction losses are not considered in Eq Equation 6.10 relates the actual flow rate to the ideal one (friction=0)

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Friction losses are not considered in Eq Equation 6.10 relates the actual flow rate to the ideal one (friction=0) Eq. 6.10 Where Cd is the discharge coefficient Substitute in Eq. 6.9 by Eq. 6.10 Eq. 6.11

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VENTURI FLOW METER Venture meter comprises a cylindrical inlet section followed by a convergent entrance into a cylindrical throat and a divergent outlet section, Fig. 6.6.

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Fig. 6.6 Venture flow meter

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Fluid passes through the convergent entrance, increasing velocity as it does so, resulting in a differential pressure between the inlet and the throat. Upstream pressure tapping is located in the cylindrical entrance section. Down stream pressure tapping is located in the throat. Flow rate can be calculated using Eq. 6.11

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ORIFICE FLOW METER A thin plate with circular orifice located in the flow duct, Fig.6.7. The differential pressure head (Δh) is measured on either sides of the orifice plate. Equation 6.11 is used to determine the flow rate.

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**FLOW VELOCITY MEASUREMENT. THE PITOT TUBE**

The pitot tube consists of a small-bore tube which is bent into the shape shown in Fig. 6.8.

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Fig Pitot tube

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It is inserted through a pressure-tight gland into the pipe-line, with its orifice, or open end, facing upstream against the direction of the flow. The fluid impacting on the tube open end will be brought to rest and its kinetic energy will be converted to pressure energy. The pressure build up in the tube will be greater than that in the free stream by an amount termed the impact pressure.

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The pressure in the pitot tube is greater than the static pressure measured at the wall of the pipe line and the difference between the two pressure (Δh) is a measure of the fluid velocity. Eq. 6.12

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Where vf is the fluid velocity, and the vpit is equal to the fluid velocity in the pitot tube which is equal to zero. The advantages of the pitot tube are that it produces only a small pressure loss in the tube, it is cheap and easy to install, and it does not interrupt the flow. The disadvantages are that, due to the small pressure differential, it is suitable only for high-velocity fluids or gases. Also, it can measure the flow rate only at a particular position in the cross-section of the pipe and it easily becomes blocked if used with a fluid carrying particles.

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