2Object At the end of this chapter the student should be able to: Describe the importance of flow sensing and its problemDescribe the principle of operation of different flow meterDescribe the constructional and mean aspects of differential meter.
3Why it is important?Almost all practical fluids engineering problems are associated with the need for an accurate flow measurement, since sometimes the material transport from place to other entails payment of financial duesThere is a need to measure :local properties (velocity, pressure, temperature, density, viscosity, turbulent intensity),integrated properties (mass flow and volume flow),global properties (visualization of the entire flow field).
4What we measure Liquid Gases Multiphase fluid Solids Custody Transfer Measuring SystemMeter measurement systemTank measuring systemMeasuring system by balance
5Local velocity measurments 1. Trajectory of floats or neutrally buoyant particles2. Rotating mechanical devicesa. Cup anemometerb. Savonius rotor c. Propeller meter d. Turbine meter3. Pitot-static tube4. Electromagnetic current meter5. Hot wires and hot films6. Laser-doppler anemometer (LDA)
6Volume-mass measurments These devices split into two classes:mechanical instruments1. Mass measurementa. Weighing tanksb. Tilting traps2. Volume measurementa. Volume tanksb. Reciprocating pistonsc. Rotating slotted ringsd. Nutating diskhead-loss instruments.1. Bernoulli-type devicesa. Thin-plate orificeb. Flow nozzle c. Venturi tube2. Friction-loss devicesa. Capillary tubeb. Porous plugThere are other widely used meters operate on different physical principles:1. Turbine meter2. Vortex meter3. Ultrasonic flowmeter
7Types of flow measuring The flow measurements can be classified into:Obstructive DeviceDifferential pressure flow meter like:Venture, orifice, pitot tubeRotameterTurbinesNon-obstructiveElectormegnaticUltrasonicCross-correlation
8Differential pressure flow meter Its widely used to measure the liquid and gasThe principle is that a restriction is placed in the pipe and the differential pressure developed across the restriction is measuredThe differential pressure output is calibrated in terms of volumetric flow rate (not mass this will need density)
91- Orifice meterThe primary element of an orifice meter is simply a flat plate containing a drilled (hole) located in a pipe perpendicular to the direction of fluid flow
13These equations for venture and orifice are valid for Turbulent flowIncompressible flowFor gases : additional expansibility factorThe values of discharge coeffiecient depends onType of flow measurement; venture and orificeDiameter ratioReynold number
14Characteristics of differential pressure measurement No moving parts, cheap, maintainableWell established, calibration availablePermanent head lossNonlinear relationship, so its not use for low pressure since the pressure has square root with velocityDischarge coefficient changes with wear, flow distributionGenerally applicable for clean fluidsInstallation constraints (for straight pipe not elbow)
15Comparison of venture and orifice VenturiorificeExpensive but offer good accuracyLeast expensiveLong working life and almost no maintenanceLow working life due to wear in the edgeCan measure flow for fluid with suspended solidUsed for clean fluid, can be used for dilute slurriesHigh rangLowest permanent head loss
163- Pitot tubeThe Pitot tube is used to measure the local velocity at a given point in the flow stream and not the average velocity in the pipe or conduit.One tube, the impact tube, has its opening normal to the direction of flow and the static tube has its opening parallel to the direction of flow.
17The fluid flows into the opening at point 2, pressure builds up, and then remains stationary at this point, called “Stagnation Point”. The difference in the stagnation pressure (impact pressure) at this point (2) and the static pressure measured by the static tube represents the pressure rise associated with the direction of the fluid.Impact pressure head = Static pressure head + kinetic energy headwhere, Cp: dimensionless coefficient to take into account deviations from Bernoulli’s equation and general varies between about 0.98 to 1.0.
18The first method, the velocity is measured at the exact center of the tube to obtain umax. then by using the Figure, the average velocity can be obtained.The second method, readings are taken at several known positions in the pipe cross section and then a graphical or numerical integration is performed to obtain the average velocity, from the following equation;
194 - The NozzleThe nozzle is similar to the orifice meter other than that it has a converging tube in place of the orifice plate, as shown in below. The velocity of the fluid is gradually increased and the contours are so designed that almost frictionless flow takes place in the converging portion; the outlet corresponds to the vena contracta on the orifice meter. When the ratio of the pressure at the nozzle exit to the upstream pressure is less than the critical pressure ratio ωc, the flow rate is independent of the downstream pressure and can be calculated from the upstream pressure alone.
20NozzleorificeExpensiveLeast expensiveLong working life and almost no maintenanceLow working life due to wear in the edgeGenerally Used to measure steamUsed for clean fluid, can be used for dilute slurriesHigh discharge coefficient = 0.99Low discharge coefficient= 0.62It has permanent head lossThe same permanent head loss since it has no diverging cone
215 Variable Area Meters – Rotameters In the Rotameter the drop in pressure is constant and the flow rate is function of the area of constriction. When the fluid is flowing the float rises until its weight is balanced by the up thrust of the fluid.Force balance on the floatGravity force = up thrust force +(drag force)Pressure forecVf ρf g = Vf ρg + (–ΔP) AfA1 : cross-section area of the tube when the float arrived.A2 : cross-section area of the annulus (flow area).
22examples1- A horizontal Venturi meter is used to measure the flow rate of water through the piping system of 20 cm I.D, where the diameter of throat in the meter is d2 = 10 cm. The pressure at inlet is N/cm2 gauge and the vacuum pressure of 35 cm Hg at throat. Find the discharge of water. Take Cd = 0.98.2- A Venturi meter is to be fitted to a 25 cm diameter pipe, in which the maximum flow is 7200 lit/min and the pressure head is 6 m of water. What is the maximum diameter of throat, so that there is non-negative head on it?3- A (30cm x 15cm) Venturi meter is provided in a vertical pipe-line carrying oil of sp.gr. = 0.9. The flow being upwards and the difference in elevations of throat section and entrance section of the venture meter is 30 cm. The differential U-tube mercury manometer shows a gauge deflection of 25 cm. Take Cd = 0.98 and calculate: -i-The discharge of oilIi-The pressure difference between the entrance and throat sections.
23examples4- An orifice meter consisting of 10 cm diameter orifice in a 25 cm diameter pipe has Cd = The pipe delivers oil of sp.gr. = 0.8. The pressure difference on the two sides of the orifice plate is measured by mercury oil differential manometer. If the differential gauge is 80 cm Hg, find the rate of flow.5- Water flow through an orifice meter of 25 mm diameter situated in a 75 mm diameter pipe at a rate of 300 cm3/s, what will be the difference in pressure head across the meter μ = 1.0 mPa.s.6- Water flow at between cm3/s through a 75 mm diameter pipe and is metered by means of an orifice. Suggest a suitable size of orifice if the pressure difference is to be measured with a simple water manometer. What approximately is the pressure difference recorded at the maximum flow rate? Cd = 0.6.
24examples7- A rotameter tube of 0.3 m long with an internal diameter of 25 mm at the top and 20 mm at the bottom. The diameter of float is 20 mm, its sp.gr. is 4.8 and its volume is 6 cm3. If the coefficient of discharge is 0.7, what will be the flow rate water when the float is half way up the tube?8- A Pitot tube is inserted in the pipe of 30 cm I.D. The static pressure head is 10 cm Hg vacuum, and the stagnation pressure at center of the pipe is N/cm2 gauge. Calculate the discharge of water through the pipe if u/umax = Take Cp = 0.98.9- A Pitot tube is placed at a center of a 30 cm I.D. pipe line has one orifice pointing upstream and other perpendicular to it. The mean velocity in the pipe is 0.84 of the center velocity (i.e. u/ux =0.94). Find the discharge through the pipe if: -i-The fluid flow through the pipe is water and the pressure difference between orifice is 6 cm H2O.Ii-The fluid flow through the pipe is oil of sp.gr. = 0.78 and the reading manometer is 6 cm H2O. Take Cp = 0.98.
256- the notch or weirIt is an obstruction in the channel that causes the liquid to back up behind it and to flow over it or through it. By measuring the height of upstream water surface, the rate of flow is determined. The velocity with which the liquid leaves depends on its initial depth below the surface.Many shapes of notch are available of which three shapes are given here as follows,6-1 Rectangular NotchTo prove this equation applies Bernoulli’s equation between points M and N as shown in Figure;The cross sectional area of flow at point Mis larger than that at notch (point N), then (uM ≈ 0)PM = PN = Po atmospheric pressureThe discharge will be:
266- the notch or weir 6-2 Triangular Notch A triangular notch is also called a V-notch.H: height of liquid abovebase of the apex of the notch.θ: Angle of the notch.tan (θ/2) = x / H = x' / (H-h)The width of the notch at liquid surface = 2x = 2H tan(θ/2)The width of the strip = 2x' = 2(H-h) tan(θ/2)The area of the strip = 2x' dh = 2(H-h) tan(θ/2)dhThe discharge is:
276- the notch or weir 6-3 Trapezoidal Notch A trapezoidal notch is a combination of arectangular notchand triangular notch as shown in Figure;Discharge over the trapezoidal notch,Q=[Discharge over the rectangular notch+ Discharge over the triangular notch]The discharge is
28examples10- A rectangular notch has a discharge of 21.5 m3/min, when the head of water is half the length of the notch. Find the length of the notch where Cd = 0.6.11- A rectangular channel 1.5 m wide is used to carry 0.2 m3/s water. The rate of flow is measured by placing a 90º V-notch weir. If the maximum depth of water is not to exceed 1.2 m, find the position of the apex of the notch from the bed of channel. Cd = 0.6.12- A trapezoidal notch 120 cm wide at top and 45 cm at the bottom has 30 cm height. Find the discharge through the notch, if the head of water is 22.5 cm. Cd1 = Cd2 = 0.6.
29Non-obstractive devices Ultrasonic flowmeters.Two examples are shown. The pulse-type flowmeter. Upstream piezoelectric transducer A is excited with a short sonic pulse which propagates across the flow to downstream transducer B. The arrival at B triggers another pulse to be created at A, resulting in a regular pulse frequency fThe same process is duplicated in the reverse direction from B to A, creating frequency . The is proportional to the flow rate.The doppler type arrangement, where sound waves from transmitter T are scattered by particles or contaminants in the flow to receiver R. Comparison of the two signals reveals a doppler frequency shift which is proportional to the flow rate. Ultrasonic meters are nonintrusive and can be directly attached to pipe flows in the field . Their quoted uncertainty of 1 to 2 percent can rise to 5 percent or more due to irregularities in velocity profile, fluid temperature, or Reynolds number.
30Hot-wire anemometer. A very fine wire (d 0 Hot-wire anemometer. A very fine wire (d 0.01 mm or less) heated between two small probes, It is ideally suited to measure rapidly fluctuating flows such as the turbulent boundary layer. The idea dates back to work by L. V. King in 1914 on heat loss from long thin cylinders. If electric power is supplied to heat the cylinder, the loss varies with flow velocity across the cylinder according to King’s lawBecause of its frailty, the hot wire is not suited to liquid flows, whose high density and entrained sediment will knock the wire right off. A more stable yet quite sensitive alternative for liquid-flow measurement is the hot-film anemometer . A thin metallic film, usually platinum, is plated onto a relatively thick support which can be a wedge, a cone, or a cylinder.
31Laser-doppler anemometer Laser-doppler anemometer. In the LDA a laser beam provides highly focused, coherent monochromatic light which is passed through the flow. When this light is scattered from a moving particle in the flow, a stationary observer can detect a change, or doppler shift, in the frequency of the scattered light. The shift f is proportional to the velocity of the particle. There is essentially zero disturbance of the flow by the laser.The advantages of the LDA are as follows:No disturbance of the flowHigh spatial resolution of the flow fieldVelocity data that are independent of the fluid thermodynamic propertiesAn output voltage that is linear with velocityNo need for calibrationThe disadvantages are that both the apparatus and the fluid must be transparent to light and that the cost is high