<p> Stem Style </p>

fca163de-9620-433d-8573-14b396f5b930 2 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Δ Re λ.f Re 2300 < 64 Re / Re 4000 < NaN Re 10 Δ / ≤ 0.3164 Re 0.25^/ Re 560 Δ / ≤ 0.11 Δ 68 Re / + (0.25^* 0.11 Δ 0.25^* if 11 line :

Re λ 2300 Re < (Re 4000 < (& λ 64 Re / : 0.3164 Re 0.25^/ Re ≤ λ 64 Re / : λ 0.11 Re 0.25^* : if if :

x λ 4000 0.25 4000 0.125 - 2 2 mat 2300 0.25 2300 0.125 - 2 2 mat 3 1 sys

Turbine Flow Metering Procedure

a 1.66 : D 1 : 12 mat a x η a x log10 * : a D x I D 2 / 2 a x η 2^a x η 1 + (2 a x η * 1 + (* / * (a x η^* : R.W. Miller [Flow Measurement Engineering Handbook] I depth of insertion [mm] wrt D ≡ 51 line

a D x I

Formulas fort the calibration procedure x η 1.66 x log10 * : D x I D 2 / 2 x η (2^x η 1 + (2 x η * 1 + (* / * (x η^* : 21 line

Calibration Procedure ... in-situ

1. Calculate Re for the nominal flow [Q]

2. Calculate the depth of insertion I(D,Re)

3. Read Q from the turbinemeter ... recalculate Re

4. Re-calculate I(D,Re) ... adjust the micrometer

5. Read Q again ... re-substitute for Re ... re-adjust

........ repeat up until the last two Q's coincide within

the stated accuraccy of the supplier ~ ± 1%

I(D,Re) is empirical and provides a quick convergence.

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Q 2400 : D 1 : ρ 1000 : μ 1 : 14 mat Re 0.353678 106^* Q * ρ D * μ * / : Vms 0.3537 Q * D 2^ρ * / : mm 1000 D Re I * : 41 line

Re Vms mm 31 mat 8.49 105^* 0.85 118.45 31 mat

Flow profile in pipes

<p> Stem Style </p>

Stem plot for QuickPlot unicolor data s i 1 data rows 1 - range vy i el data i el data i 1 + (1 el 1 el 012 mat stack : for V vy 1 el : j 2 data rows 1 - range V V vy j el stack : for V 41 line :

Prepare stem style data S stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for stem 31 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Turbulent: Q2, Q3 L 1 - : H 1 : N 199 : 13 mat U L H N xd : 21 line

n 0.875 0.125 0.05 13 mat transpose : n x Profile x 1 + (x 1 - (* - (n^: 21 line

j Q i 1 U rows range vx i el U i el : vy i el n j el U i el Profile : 21 line for vx vy augment 21 line :

Q1 1 Q : laminar ≡ Q2 2 Q : mid turbulent ≡ Q3 3 Q : high turbulent ≡ 31 line

Stem style codes

Observe laminar => Q(1)
to capture N 29 stems
laminar Q1 captures N 199 L 1 - : H 1 : N 49 : 13 mat U L H N xd : laminar 1 Q : 31 line

Observe: laminar Q(1) collects N 49 stems laminar Q1 collects N 199 stems

What you see on the graph is purely suggestive.

laminar laminar 1 col 1 laminar 2 col * augment :

data laminar S : stem data s : 21 line

plot laminar Q2 Q3 stem 51 sys :

Flow profile: laminar, turbulent

plot

a 1.66 : D 1 : 12 mat a x η a x log10 * : a D x I D 2 / 2 a x η 2^a x η 1 + (2 a x η * 1 + (* / * (a x η^* : R.W. Miller [Flow Measurement Engineering Handbook] I depth of insertion [mm] wrt D ≡ 51 line

1.66 D x I 1.8 D x I 1.5 D x I 3 1 sys

XY 15 0.121229 135 0.119489 635 0.118596 32 mat :

x β f β 1 el β 2 el β 3 el x + / + :

β 0.118226 0.261316 71.974909 31 mat :

FIT x 010001 range : i 1 x rows range FIT i el x i el β f eval : for x FIT augment 31 line :

FIT XY XY 3 1 sys