Volume Flow Measurements Obstruction Meters Orifice Meters Venturi

Volume Flow Measurements Obstruction Meters Orifice Meters Venturi

Volume Flow Measurements Obstruction Meters Orifice Meters Venturi Meters

Flow Nozzles Flow through a Nozzle Basic Equations: 1 m 2 m Av m a.) Continuity: mass in = mass out

b.) Bernoullis Eqn. 1A1 v1 2 A 2 v 2 incompressible 1 2 A1 v1 A 2 v 2 Total pressure is constant throughout 1 m

2 m 1 2 A1 v1 A2 v2

Flow through a Nozzle Bernoulli P0 Total Pr essure const. 1 2 v P 2 1 1 2 2 1 v1 P1 2 v 2 P2 P0 2 2

P static pressure P0 total pressure 1 2 v dynamic pressure 2 Flow through a Nozzle v2 1 A2 1

A1 Flow Rate Q A 2 v 2 A 2 2 P 2 1 A2 1 A1

2 2 P For Re al Flow Q YCA 2 1 A2 1 A1

2 2 P Ideal Flow through a Nozzle 1 1 P P1 P2 2 v22 1v12

2 2 2 1 1 A2 2 2 2 v2 1 v2 2 2 A1 1 2 v 2 1 2

when 1 2 2 A2 A1 P Flow through a Nozzle

Y= Compressibility Factor =1 for incompressible flow or when P<< Pabs C= Discharge Coefficient =f(Re) and nature of specific flow meter P

P Flow through a Venturi Meter In a venturi, 0.95 < C < 0.98 Advantage: Pressure recovery Uses little power Flow through a Venturi Meter 0.98 C

2 x 105 Re d 1 v1 R e Based upon the conditions in the pipe approaching the meter

Back to the Nozzle P1 P2 P1 P P2 The Nozzle Flowmeter Shorter and cheaper than venturi But larger pressure drop. Thus, more power lost in operating.

0.98 C 0.86 10 3 Re 105

Flow Through an Orifice Meter Flow Through an Orifice Meter P1 P2 d P1

P D Flow Through an Orifice Meter -Cheapest and Simplest -But biggest pressure drop and power lost (C~0.6 - 0.7) -Side Note: Pressure drop caused by friction and turbulence of shear layer downstream of vena contracta

Re 0.85 1 C CM 2

A2 1 A1 0.6 10k 5000 100k 0.1

=d/D 0.8 Elbow Flowmeter Laminar Flowmeter Pitot-Static Tubes Rotameter, variable-areaflowmeter

Force balance Drag Force Gravity Buoyancy (usually negligible)

m use m cal Derived on next slide use cal Rotameter Equations m A V V2 F D

Mg 2 2 Mg V D 2 Mg 2 MgA2 m A D D For a fixed x-position, A is fixed. Then

m m use cal m use m cal use

cal Turbine Flow Meters Vortex meters operate on the principle that when a non-streamlined object is placed in the middle of a flow stream, vortices are shed alternately downstream of the object. The frequency of the vortex shedding is directly proportional to the velocity of the liquid flowing in the pipeline. Magnetic flowmeter Magnetic flowmeter

Based upon Faradays Law The fluid is the conductor, must be electrically conductive. E=BDVx10-8 E=voltage, volts B=magnetic flux density, gauss D= length of the conductor, cm V=velocity of the conductor, cm/sec Magnetic Flow Meter Coriolis Mass Flow Meter

Coriolis Mass Flow Meter Flow Flow Force Flow Flow Force Vibrating Flow Tube Fluid Force is Reacting to Vibration of Flow Tube

Twist Angle Twist Angle End View of Flow Tube Showing Twist Coriolis Mass Flow Meter Positive Displacement Meters

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