Flow Rate Measurement Techniques in Fluid Mechanics

1. Measurements in Fluid Mechanics058:180 (ME:5180)Time & Location: 2:30P - 3:20P MWF 3315 SCOffice 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

2. Lecture 14. Flow rate measurement

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

4. Flow rate measurement Positive-displacement (PD) flow meters - devices that isolate fixed volumes of fluid flowing into their inlet in sealed compartments and then discharge them to the outlet. - 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. - some PD meters (metering pumps) are driven by external power source to create fluid motion. - a great variety of designs of PD meters, classified as rotary, reciprocating, or nutating - PD meters for liquids - problems of PD flow meters: leakage and pressure loss 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 nutatingfashion in a dual conical housing

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

7. Flow rate measurement Rotary-piston (oscillating piston ) flow meters - a cylindrical drum mounted eccentrically inside a cylindrical housing 7

8. 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 8

9. Flow rate measurement Rotor meters Oval Gear Meters

10. Flow rate measurement Rotor meters Gear flow meters

11. Flow rate measurement Rotor meters Helical gear flow meter

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

13. Flow rate measurement Diaphragm-type meters

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) Dall tubes (c) Flow nozzles (d) Orifice-plate (e) - Circular tube of diameter D - Smaller diameter d in restriction to increase velocity & result in pressure drop - Ideal volume rate determined by continuity & Bernoulli’s equation : - Measured volume rate with empirical discharge coefficient :

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

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

18. Try to write a Matlab program • To cut a 64×64-pixel image sample from a 1280×1024-pixel image at i=200, j=400 64×64-pixel image sample clear; A1=imread('A001_1.bmp'); [nxny]=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 end imwrite(G1,'G1.bmp','bmp') http://lcgui.net/ui-lecture2012/hw/00/A001_1.BMP • To cut a 64×64-pixel image sample from a 1280×1024-pixel image at X=400.6, Y=200.3