Flow meters

Diff i l P MDifferential Pressure Meters

Differential pressure meters are widely used in industrial applicationsand laboratories because of their simplicity, reliability and low cost.

Three commonly used types are:orifice meter, venturi meter, and flow nozzle.

Their operation is based on the principle of an obstruction to flowbeing present in a duct or pipe, and consequently, a pressuredifferential will exist across the obstruction.

This pressure drop can be correlated to the discharge by means of acalibration, and subsequently, the pressure-discharge curve can beused to determine the discharge by reading the differential pressure.g y g p

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The above Figure shows a thin-plate orifice meter, which can beconsidered as a representative differential pressure meter. Consider at d fl i i l d t t th t i ti ifi ithsteady flow in a circular duct encounters the restrictive orifice with

area A0, and issues as a downstream jet. Downstream of therestriction, the flow converge to form a minimal flow area Ac, termedh l d i ithe vena contracta. Pressure taps are located at two positions:

upstream of the restriction in the undisturbed flow region (location l)and downstream at some location in the vicinity of the vena contracta(location 2). Assuming an ideal, frictionless, incompressible fluid, theBernoulli equation applied along the center streamline from

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Other Types of Flow MetersOther Types of Flow Meters

Turbine Meter: The turbine meter consists of a propeller mountedinside a duct that is spun by the flowing fluid The propeller's angularinside a duct that is spun by the flowing fluid. The propeller s angularspeed is correlated to the discharge. They are commonly employed tomonitor flow rates in fuel supply lines.

Rotameter: The rotameter consists of a tapered tube in which theflow is directed vertically upward (Fig. 13.14). A float moves upwardor downward in response to the flow rate until a position is reached

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or downward in response to the flow rate until a position is reachedwhere the drag force on the float is in equilibrium with its submergedweight.

Through calibration the vertical elevation of the float is correlatedwith the discharge. With appropriate design, the float position canbe made linearly proportional to the discharge. The rotameter does

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not provide accuracy as good as the differential pressure meters;typically it is in the range of 5% full scale.

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Problem: Calculate the flow rate of 40oC water in the pipe shown. Take Cd = 0.995.SolutionApplying Continuity Equation between points 1 and 2A1V1 = A2V2 => V2 = A1V1/A2 = (12/6)2xV1=4V1

From manometry, p1+γ (h+0.12)=p2+γh+γHg0.12=>(p1-p2)/γ =0.12(γHg-γ)=0.12(13.6-1) =1.512 m of water

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Applying Bernoulli’s Equation between points 1 and 2p1/γ+V1

2/2g+z1 = p2/γ+V22/2g+z2

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Taking z1 = z2, we have, p1/γ+V12/2g = p2/γ+V2

2/2gg 1 2, , p1 γ 1 g p2 γ 2 g⇒V2

2/2g – V12/2g = (p1-p2)/γ = 1.512 m

⇒(4V1)2/2g – V12/2g = (p1-p2)/γ = 1.512 m

⇒15V12/2g = 1.512 m⇒15V1 /2g 1.512 m

⇒V1 = 1.41 m/s⇒The theoretical flow rate Qt = A1V1 = π(0.12/2)2x 1.41 = 0.016 m3/s

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⇒Now the actual flow rate Qa = CdQt = 0.995x 0.016 = 0.0159 m3/s

Problem: Calculate the flow rate of 40oC water in the pipe shown. Take Cd = 0.6.

Answer: 0.0096 m3/s

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