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 Phone: (Lab), (Cell)

2 Lecture 14. Flow rate measurement

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

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

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

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

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

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

9 Flow rate measurement Rotor meters Oval Gear Meters

10 Flow rate measurement Rotor meters Gear flow meters

Helical gear flow meter 11 Flow rate measurement Rotor meters

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

Flow rate measurement Diaphragm-type meters 13

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

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 :

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

17 Homework - Questions and Problems: 1 on page Read textbook on page Due on 09/28

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 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