Chapter 10 Notes - Chapter 10 Flow Measurements Material...

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1 Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate ± Flow rate can be expressed in terms of volume flow rate (volume/time) or mass flow rate (mass/time). ± Flow rate through pipe or duct can be defined using concept of control volume, where the amount of flow through volume in a given period of time is the flow rate. Figliola, 2000 Flow Rate ± The velocity of the flow is described at any point by: ± u, v, and w are scalar velocity magnitudes and are unit vectors. ± By conservation of mass, the amount of fluid density ρ that passes through control volume (CV) and accumulates within CV must be equal to 0. ϑ ^ , ^ , ^ e e e r x ϑ + + = ϑ ^ ^ ^ ) , , ( e w e v e u r x U r x
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2 Flow Rate ± For steady flows, ± where ± is mass flow rate through area A ± For isometric flows, consider liquids as incompressible. ± Q in =Q out where ± Where Q is the volumetric flow rate out o in o m m = ∫∫ ρ = A o dA n u m ^ * o m dA n u Q A ∫∫ = ^ * Flow Rate ± In pipe flow, if we know u(r, ϑ ) at position x, in steady, incompressible flow, we can estimate the average velocity and, thus, average flow. ± ± r 1 is the pipe radius. ∫∫ π ϑ ϑ = 1 0 2 0 r dr rd r u Q ) , ( Flow Rate ± If the average velocity is known, Q = A. ± A method that will measure steady flow rates must be sensitive to either average mass flux or average velocity U ρ __ U __ U . __ U
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3 Flow Rate ± The flow in a pipe is either laminar, turbulent, or transitional. ± Using Reynolds number, ± Turbulent flow: R e > 4000 v = kinematic viscosity ± Laminar flow: R e < 2000 ± d 1 = diameter for circular pipe or hydraulic diameter (4r h ) for non-circular cross- sections. ± r h = wetted area/ wetted parameter ± Note: Stay away from transitions in flow v d Q v d U R e 1 1 4 / π = = Volume Flow Rate ± The direct implementation of equations for estimating the volume flow rate through a duct requires measurement of the velocity at points along several cross-sections of a flow control surface. ± This procedure is most often used for the one-time verification or calibration of system flow rates. Volume Flow Rate ± In using this technique in circular pipes, a number of discrete measuring positions are chosen along “ m” flow cross-sections (radii) spaces at 360 o / m apart. ± A velocity probe is traversed along each flow cross-section with readings taken at each measurement position.
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4 Figliola, 2000 Obstruction Flow Meters ± Three types of meters that use obstruction: 1. Orifice plate 2. Venturi 3. Flow Nozzle Obstruction Flow Meters ± Obstruction flow meters rely on the Bernoulli effect. When a restriction in flow occurs, there is an increase in velocity (conservation of mass). When velocity goes up, pressure goes down.
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Chapter 10 Notes - Chapter 10 Flow Measurements Material...

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