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Pressure Flow Through a Coiled Tube

Group M5

BE 310 Spring 2004

Amy Garber

Liani Hernandez

Chris MullinMelissa Simon

bs!ra"!

Pressure Flow experiments were performed on coiled tubin to in!estiate the effects of

coil orientation" radius of cur!ature" and fluid !iscosity on the flow# From Poiseuille$s

Law and theories and experiments of %#H# &ean and C#M# %hite" a relationship betweenpressure and the &ean 'umber (&e ) *d+, (d+&-.+/-" was determined to be Pd/+L0*

)1/(2#13&e2#14-# From this relationship" a plot of the non5dimensionalized pressure

!ersus the function of the &ean 'umber should ha!e a slope of 1/# Coil orientation

experiments showed that the slope for the horizontal descendin orientation" 1.#16 7 3#/8and is the only one that o!erlaps 1/" and is the orientation that most minimizes the effects

of ra!ity# 9he experiments !aryin radii of cur!ature" tubin of .#3 cm and .8#1/ cmradii of cur!ature had slopes of 1.#:1 7 .#1; and 18#18 7 /#/1" respecti!ely# For a .2ssentials of Fluid &ynamics# Hafner Publishin Company ('ew

or= .:6/-# :;5::" .4.5.4;#

91 Final Beport" K> 1.2# Measurement of Pressure5Flow Belationship in a Cur!ed

9ubeE# Sprin /22/#

M6 >xperiment /" K> 1.2# Measurement of the Pressure5Flow Belationship in a

Straiht" Horizontal 9ubeE# Sprin /228#

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ppendi

9wo other methods of data analysis were attempted and both had little success# 9he firstmethod in!ol!ed a non5dimensional approach to this problem" usin the >uler number

NP+Ou/" as the non5dimensionalized !ersion of pressure# From this approach of

dimensional analysis" the >uler number is e?ual to some function of lenth" diameter" and&ean 'umber# Ky remo!in a non5dimensional lenth from this function" we ha!e the

e?uation NP+Ou/) L+d f(&e-# As shown in 9able /" this function of the &ean 'umber is

not e?ual to the C#M# %hite$s experimental function f(&e- ) 2#13&e2#14# 9his newfunction could be determined experimentally" but this is well beyond the scope of the

proJect" and would re?uire much further experimentation#

Radi#s o$%#rvat#re

&c"'(

&")sec' *# &*#+,')- $&,e'

1.70 0.12 492.93 0.11 2.18

0.11 498.29 0.11 2.11

0.09 571.39 0.13 1.960.07 659.79 0.15 1.80

0.05 741.09 0.17 1.61

0.02 938.49 0.21 1.19

5.40 0.02 1933.85 0.44 0.87

0.05 811.33 0.18 1.30

0.07 652.08 0.15 1.46

0.10 513.11 0.12 1.64

0.12 447.10 0.10 1.74

0.13 420.87 0.10 1.81

14.32 0.03 653.64 0.15 0.890.07 527.43 0.12 1.20

0.09 452.56 0.10 1.31

0.11 375.53 0.09 1.45

0.13 350.83 0.08 1.52

0.15 329.79 0.07 1.60

4.04 0.03 988.00 0.22 1.07

0.05 772.45 0.17 1.39

0.07 668.52 0.15 1.53

0.10 559.50 0.13 1.71

0.11 518.07 0.12 1.80

0.12 504.35 0.11 1.85

Table 2$ Coparison o& !he nondiensionalied pressure -P.'(6u 2/ !o !he &-.e/,

Sin"e "oluns !hree and &our are no! e7ual8 !he &-.e/ &or !his nondiensionalied

pressure is no! e7ual !o &-.e/ 9 0,3:.e0,3;,

A second approach to the data analysis would be to non5dimensionalize the pressure in

the form of head loss" e?ual to hL) NP+O ) (1/0*L+Od/- I f(&e-# 9his function of the

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&ean 'umber is also not the one defined by C#M# %hite$s experimental function f(&e- )

2#13&e2#14# 9his function could similarly be determined experimentally" but this would

re?uire more trials and is well outside the scope of the proJect#

Radi#s o$%#rvat#re

(&")sec' )/g 32(-)gd2'+$&,e' di$$

1.70 0.12 0.75 1.04 38.47

0.11 0.64 0.92 44.85

0.09 0.48 0.69 44.34

0.07 0.34 0.50 45.89

0.05 0.21 0.33 57.33

0.02 0.05 0.10 113.79

5.40 0.02 0.06 0.06 0.62

0.05 0.22 0.26 18.73

0.07 0.34 0.41 19.89

0.10 0.51 0.63 23.71

0.12 0.62 0.79 27.75

0.13 0.72 0.91 26.71

14.32 0.03 0.06 0.10 77.49

0.07 0.25 0.32 28.62

0.09 0.34 0.44 28.45

0.11 0.51 0.65 28.65

0.13 0.61 0.78 26.79

0.15 0.75 0.93 24.06

4.04 0.03 0.07 0.11 59.81

0.05 0.23 0.29 27.85

0.07 0.34 0.42 23.95

0.10 0.52 0.64 21.96

0.11 0.64 0.77 20.52

0.12 0.74 0.86 17.25

Table 3$ Coparison o& !he !wo e7ua!ions o& head loss, Colun &our "opares !he

s!andard de&ini!ion o& head loss8 P'pg8 wi!h -32)*('6gd2/ < &-.e/, The large per"en!

di&&eren"es show !ha! !he &-.e/ o& 0,3:.e0,3;does no! appl in !his e7ua!ion,