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
Lecture 14. Flow rate measurement
2
Flow rate measurement
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
- not concerned with short-time (turbulent) fluctuations
Volume flow rate Q – usually used for liquids or low-speed gasses
Mass flow rate
Direct methods for flow rate measurement
Vn
- measure typical flow velocity, i.e.
𝑄 = 𝑉 ∙ 𝐴 𝑜𝑟 𝑄 =
𝐴
𝑉𝑛 𝑑𝐴
A
- measure amount of discharged fluid over a period of time, i.e.
𝑚=
𝑚
𝐶
𝑜𝑟 𝑄 =
∆𝑡
∆𝑡
C – volume of fluid
- positive-displacement flow meters
3
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
- 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
4
Flow rate measurement
Nutating disk meters
- a disk rotating in a nutating fashion in a dual conical housing
5
Flow rate measurement
Reciprocating -piston meters
- plunger or piston driven by wobble plate (or cam)
single piston reciprocating
6
Flow rate measurement
Rotary-piston (oscillating piston ) flow meters
- a cylindrical drum mounted eccentrically inside a cylindrical housing
7
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
Flow rate measurement
Rotor meters
Oval Gear Meters
9
Flow rate measurement
Rotor meters
Gear flow meters
10
Flow rate measurement
Rotor meters
Helical gear flow meter
11
Flow rate measurement
Roots-type flow meters
- a particular design of a lobe meter
Lobe Rotary Piston
12
Flow rate measurement
Diaphragm-type meters
13
Flow rate measurement
Liquid-sealed flow meters
- wet gas meters: liquid provides sealing action
Liquid ring pump
14
Flow rate measurement
Restriction (or obstruction) flow meters
∆𝑝
𝐷
Venturi tubes (a & b)
Dall tubes (c)
Flow nozzles (d)
𝑑
Orifice-plate (e)
- Circular tube of diameter D
- Smaller diameter d in restriction to increase velocity & result in pressure drop ∆𝑝
- Ideal volume rate determined by
continuity & Bernoulli’s equation :
- Measured volume rate with empirical
discharge coefficient 𝐶𝑑 :
15
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
16
Homework
- Read textbook 9.1-9.4 on page 208 - 212
- Questions and Problems: 1 on page 219
- Due on 09/28
17
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
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
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
end
imwrite(G1,'G1.bmp','bmp')
18