ABB AquaMaster4 Operating Instructions Manual

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ABB AquaMaster4 Operating Instructions Manual Manual pdf 28 page image

28A Q U A M A S T E R 4 | E L E C T R O M A G N E T I C F LO W M E T E R I N S E R T I O N S E N S O R | O I/ F E W 4 0 0/A P - E N R E V. B…AppendixVelocity profiles backgroundThe Point of Mean Velocity is on the knee of the curve (thevelocity at this point is changing rapidly with distance) so it isnecessary to position the insertion sensor extremely accuratelyin order to measure the correct velocity. If the insertion sensoris inserted accurately to 72.5 mm, it is therefore measuring themean velocity of 1.722 m/s which, when multiplied by the area,gives a volume flow of 487 l/s. If the insertion sensor is insertedto 74 mm instead of 72.5, the velocity measurement is 1.85 m/sinstead of the expected 1.722. Multiplying this figure by thearea results in a volume flow of 523 l/sec – an error of 7.4 %.On-site it can be very difficult to locate a insertion sensorexactly, so this sort of error is quite common. With insertionsensors other than this insertion sensor, working under anydegree of pressure in the line, inserting a insertion sensor towithin 10 mm of its intended location is often accepted. Usingthe calculation above, this produces an error of approximately15 %. This can be reduced significantly by using the followingmethod.Referring to Figure 28, in the middle of the pipe, near the centerline, the profile is relatively flat, i.e. the flow velocity does notchange very much with distance into the pipe. Therefore, if thevelocity is measured on the center line, measurement errorsdue to positional errors (i.e. not locating the insertion sensorwhere required) are very small; hence most users will try to usethe center line measuring position. However, as explainedpreviously, this process gives us the wrong answer, Fortunatelythere is a mathematical relationship between the velocity at thecenter line and the mean velocity within the pipe – the ProfileFactor (Fρ).The value of Fρ can be calculated by an equation (below) orobtained from a graph – see Figure 29.Fρ is calculated as follows:where:and:n = 1.66log(R)and:DR = –ρνμkey:D = pipe diameterρ = fluid densityν = average fluid velocityμ = fluid viscosityPipe bore in mmPipe bore in inchesProfile factor (Fp)200 400 600 800 1000 1200 1400 1600 1800 200080.875 16 24 32 40 48 56 64 72 800.8700.8650.8600.8550.850Figure 29 Profile factor vs flow velocity for pipe sizes200 to 2000 mm (8 to 78 in)When the insertion sensor insertion position is determined, theeffect of putting the insertion sensor into the pipe (see page27) must be calculated.The blockage or insertion effect is termed the Insertion Factor(Fi). This is a mathematical relationship and can be calculatedfrom the formula:Testing the flow profile for symmetryIf there is any doubt as to the symmetry of the flow profile (seepage 10), a Partial Velocity Traverse must be carried out.This procedure involves comparing the value of velocity at twopoints at equal distances from the center line.It is normal to compare the flow velocities at insertion depthsof 1/8 and 7/8 of the pipe diameter as these points are always onthe 'knee' of the profile.Partial velocity traverseDetermine the internal diameter D of the pipe, in millimeters, bythe most accurate method available. If the insertion sensorinsertion length is greater than the internal diameter of thepipe, proceed with the Single Entry Point Method. If theinsertion sensor’s insertion length is less than the internaldiameter of the pipe, proceed with the Dual Entry PointMethod.F 1 (r – Y)r= ––1nρYb r (n + 1) (2n + 1)2n= Fi = 11 – (38/(πD))