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 15. Flow rate measurement

3 Flow rate measurement Averaging Pitot tubes - a tube spanning the cross section of the pipe - multiple frontal openings for averaged total pressure - second tube facing backwards to measure static pressure

4 Flow rate measurement Laminar flow elements - contain tube bundles or long honeycombs - create laminar flow with Re< linear response between flow rate and pressure drop

5 Flow rate measurement Rotameters (variable-area flow meters) - vertical tube with cross section increasing linearly upwards - a float at a position with drag, buoyancy and weight in balance - height of float proportional to flow rate

6 Flow rate measurement Vortex-shedding flow meters - a bluff object results in periodic shedding of vortices - vibration frequency (f) measured downstream - constant Strouhal number with Re>5000: - S= , dependent on shape of the bluff body h – front width of the bluff V – flow velocity Drag (target) flow meters - bluff object immersed in flow - drag force F D measured - flow velocity determined by - flow rate given as k – constant depending on the structure

7 Flow rate measurement Turbine flow meters - an immersed rotor with vanes - angular velocity measured with pulse counter - flow rate proportional to angular velocity k – constant n – number of pulses per unit time Paddle-wheel flow meters - axis normal to flow direction

8 Flow rate measurement Ultrasonic flow meters - frequency change used to calculate flow velocity - use sound waves to measure flow rate of fluid - 2 piezoelectric crystals: transmitter & receiver Doppler flow meters Time-of-flight flow meters - solid particles or gas bubbles reflect ultrasound - frequency difference used to determine velocity - Two pairs of transmitter & receiver - sound pulse transported by flowing fluid - located upstream and downstream - independent of sound speed (temperature) - Doppler shift: f t – transmitted frequency f r – received frequency c – sound speed  – measurement angle l – distance between transducers

9 Flow rate measurement Electromagnetic (magnetic, induction) flow meters - conductive fluid passing across a controlled magnetic field - flow velocity obtained by measuring changes of induced voltage Coriolis flow meters - flow guided into U-shaped tube - twist induced to the tube by Coriolis acceleration - time delay  t between motions of two legs measured - flow rate determined accordingly k – numerical coeficient B – magnetic flux density D – pipe diameter E – electric potential - mass flow rate related as r t – radius of the tube K S – constant

10 Flow rate measurement Thermal flow meters Heated-tube flow meters Immersion-probe flow meters - flowing gas passed electrically heated tube - temperature measured up- and down stream - heat transfer rate related to mass flow rate C p – specific heat under constant pressure - two resistance temperature detectors (RTDs) - one RTD used to measure gas temperature - another heated with current to higher temperature - electric power related non-linearly to  V

11 Flow rate measurement Selection of flow meters

12 Homework - Questions and Problems: 2 on page Read textbook on page Due on 10/01

13 Matlab function for transferring image coordinate (i,j) to physical coordinates (x,y) Learn to write a Matlab program function [G]=img2xy(A) % A - image % G - gray value distribution [ny nx]=size(A); for x=1:nx for y=1:ny G(x,y)=A(ny-y+1,x); end nx – number of columns, ny – number of lines x = ny-j+1, y=i x y j i

14 Matlab function for transferring physical coordinates (x,y) to image coordinate (i,j) Learn to write a Matlab program function [A]=xy2img(G) % A - image % G - gray value distribution [nx ny]=size(G); Gmax=max(max(G)); Gmin=min(min(G)); for x=1:nx for y=1:ny A(ny-y+1,x)=uint8(double(G(x,y)-Gmin)/double(Gmax-Gmin)*245+5); end nx – number of columns, ny – number of lines j=ny-x+1, i=y

15 Matlab function for selecting an interrogation sample from an image for i=1:M for j=1:N ii=i+I-int16(M/2); jj=j+J-int16(N/2); if ii>=1 & ii =1 & jj<ny Ga=double(G(ii,jj)); Gb=double(G(ii+1,jj)); Gc=double(G(ii,jj+1)); Gd=double(G(ii+1,jj+1)); A=(1-x)*(1-y); B=x*(1-y); C=(1-x)*y; D=x*y; g(i,j)=A*Ga+B*Gb+C*Gc+D*Gd; % bilinear interpolation gm=gm+g(i,j); nr=nr+1; else g(i,j)=-1; end gm=gm/double(nr); for i=1:M for j=1:N if g(i,j)<0 g(i,j)=gm; end function[g]=sample01(G,M,N,X,Y) %INPUT PARAMETERS % G - gray value distribution of the PIV recording % M - interrogation sample width % N - interrogation sample height % X, Y - interrogation sample coordinates % % OUTPUT PARAMETERS % g - gray value distribution of the evaluation sample % % I, J – integer part of evaluation sample coordinates % x,y – decimal part of evaluation sample coordinates [nx ny]=size(G); I=int16(X); J=int16(Y); x=double(X)-double(I); y=double(Y)-double(J); if x<0 I=I-1; x=x+1; end if y<0 J=J-1; y=y+1; end gm=0; nr=0;

16 To cut a 64×64-pixel image sample from a 1280×1024-pixel image at X=400.6, Y=200.3 Learn to write a Matlab program 64×64-pixel image sample clear; A1=imread('A001_1.bmp'); G1=img2xy(A1); M=64; N=64; x=400.6; y=200.3; g1=sample01(G1,M,N,x,y); A2=xy2img(g1) imwrite(A2,'G2.bmp','bmp')