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Measurements in Fluid Mechanics 058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

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2 Lecture 14. Flow rate measurement

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Bulk flow rate 3 Flow rate measurement - the amount of fluid that pass through a certain cross section of a pipe, duct, channel, or other conduit per unit time. Mass flow rate Direct methods for flow rate measurement A VnVn - measure typical flow velocity, i.e. - measure amount of discharged fluid over a period of time, i.e. C – volume of fluid - positive-displacement flow meters Volume flow rate Q – usually used for liquids or low-speed gasses - not concerned with local velocity variations across cross-section - not concerned with short-time (turbulent) fluctuations

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4 Flow rate measurement Positive-displacement (PD) flow meters - volume flow rate calculated from the size and number of compartments and the repetition rate - some PD meters may passively receive power from flowing fluid to operate. - devices that isolate fixed volumes of fluid flowing into their inlet in sealed compartments and then discharge them to the outlet. - a great variety of designs of PD meters, classified as rotary, reciprocating, or nutating - some PD meters (metering pumps) are driven by external power source to create fluid motion. - problems of PD flow meters: leakage and pressure loss - PD meters for liquids Nutating disk meters, reciprocating-piston meters, rotary-piston meters, rotary-vane meters, rotor meters - PD meters for gases Roots-type meters, diaphragm-type meters, liquid-sealed drum-type meters

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5 Flow rate measurement Nutating disk meters - a disk rotating in a nutating fashion in a dual conical housing

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6 Flow rate measurement single piston reciprocating Reciprocating -piston meters - plunger or piston driven by wobble plate (or cam)

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77 Flow rate measurement Rotary-piston (oscillating piston ) flow meters - a cylindrical drum mounted eccentrically inside a cylindrical housing

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88 Flow rate measurement Rotary-vane flow meters - flat vanes inserted into matching slots around the perimeter of a cylindrical drum located eccentrically within the housing

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9 Flow rate measurement Rotor meters Oval Gear Meters

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10 Flow rate measurement Rotor meters Gear flow meters

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Helical gear flow meter 11 Flow rate measurement Rotor meters

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12 Flow rate measurement Roots-type flow meters - a particular design of a lobe meter Lobe Rotary Piston

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Flow rate measurement Diaphragm-type meters 13

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14 Flow rate measurement Liquid-sealed flow meters - wet gas meters: liquid provides sealing action Liquid ring pump

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15 Flow rate measurement Restriction (or obstruction) flow meters Venturi tubes (a & b)Flow nozzles (d)Dall tubes (c)Orifice-plate (e) - Circular tube of diameter D - Ideal volume rate determined by continuity & Bernoulli’s equation :

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16 Flow rate measurement Open-channel flow measurement - Weirs of sharp crested and broad crested with rectangular, v-shaped or trapezoidal openings - Flow rate over weirs: - full angle of the V-notch Weirs Venturi flumes - converging-diverging channel constructions

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17 Homework - Questions and Problems: 1 on page 219 - Read textbook 9.1-9.4 on page 208 - 212 - Due on 09/28

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18 To cut a 64×64-pixel image sample from a 1280×1024-pixel image at i=200, j=400 Try to write a Matlab program http://lcgui.net/ui-lecture2012/hw/00/A001_1.BMP 64×64-pixel image sample clear; A1=imread('A001_1.bmp'); [nx ny]=size(A1); I=200; J=400; M=64; N=64; for i=1:M for j=1:N ii=i+I-int16(M/2); jj=j+J-int16(N/2); G1(i,j)=A1(ii,jj); end imwrite(G1,'G1.bmp','bmp') To cut a 64×64-pixel image sample from a 1280×1024-pixel image at X=400.6, Y=200.3

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