| Topic: |
Science > Physics |
| User: |
"Andy Resnick" |
| Date: |
22 Aug 2006 01:06:33 PM |
| Object: |
Q: drag force on a cylinder |
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "cnctut" |
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| Title: Re: Q: drag force on a cylinder |
22 Aug 2006 06:02:05 PM |
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Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Andy,
If you write Cd as given by Stokes law as a function of Reynolds
numbers in the the stardard drag equation, you will get a log term in
the equation--at least for Reynolds numbers below 100. Does this help?
Tut
Tut
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| User: "cnctut" |
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| Title: Re: Q: drag force on a cylinder |
22 Aug 2006 07:31:20 PM |
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cnctut wrote:
Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Andy,
If you write Cd as given by Stokes law as a function of Reynolds
numbers in the the stardard drag equation, you will get a log term in
the equation--at least for Reynolds numbers below 100. Does this help?
Tut
Andy,
Here's some approximate data points for you using Stokes:
Renolds # Cd
2 15
5 6
10 3.5
100 .44
Looks like a straight line on a logarithmic scale. 'Plot Cd vs
Renolds--write the equation for the data points Cd (Ren) = and you
should be on your way towards an answer if Ren<100.
Thats about the best I can do--hope this helps,
Best Wishes,
Tut
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| User: "tadchem" |
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| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 04:28:56 AM |
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cnctut wrote:
Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Andy,
If you write Cd as given by Stokes law as a function of Reynolds
numbers in the the stardard drag equation, you will get a log term in
the equation--at least for Reynolds numbers below 100. Does this help?
Stokes' Law was derived for spheres. The OP specified cylinders. They
are different. See figure 2:
http://www.princeton.edu/~asmits/Bicycle_web/blunt.html
Semi-empirical equations of the type used by engineers are likely to
give better results, if properly used.
Tom Davidson
Richmond. VA
.
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| User: "cnctut" |
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| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 06:22:47 AM |
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tadchem wrote:
cnctut wrote:
Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Andy,
If you write Cd as given by Stokes law as a function of Reynolds
numbers in the the stardard drag equation, you will get a log term in
the equation--at least for Reynolds numbers below 100. Does this help?
Stokes' Law was derived for spheres. The OP specified cylinders. They
are different. See figure 2:
http://www.princeton.edu/~asmits/Bicycle_web/blunt.html
Semi-empirical equations of the type used by engineers are likely to
give better results, if properly used.
Tom Davidson
Richmond. VA
.
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| User: "cnctut" |
|
| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 06:31:21 AM |
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tadchem wrote:
cnctut wrote:
Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Andy,
If you write Cd as given by Stokes law as a function of Reynolds
numbers in the the stardard drag equation, you will get a log term in
the equation--at least for Reynolds numbers below 100. Does this help?
Stokes' Law was derived for spheres. The OP specified cylinders. They
are different. See figure 2:
http://www.princeton.edu/~asmits/Bicycle_web/blunt.html
Semi-empirical equations of the type used by engineers are likely to
give better results, if properly used.
Tom Davidson
Richmond. VA
//
Tom,
Thanks for the info. ;-)
Tut
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| User: "tadchem" |
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| Title: Re: Q: drag force on a cylinder |
22 Aug 2006 04:30:48 PM |
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Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
My Eshbach (Handbook of Engineering Fundamentals) gives the drag force
D for a body immersed in an incompressible fluid in terms of the drag
coefficient C, the fluid free-stream density r, the free-stream
velocity V and the 'characteristic' area of the body S as
D = C*r*V^2*S/2
and in a table gives C for a circular cylinder perpendicular to the
flow for a Reynolds number Re of 10^5 and a variety of aspect ratios
(cylinder length/diameter):
L/d C
1 0.63
5 0.74
20 0.90
A separate graph gives D for a variety of Reynolds numbers for an
'infinite' cylinder as
Re C
0.1 60
1.0 10
10 2.5
100 1.5
1000 1..0
My Perry's (Perry's Chemical Engineer's Handbook) gives a formula for C
for rigid spherical particles only, but the graph shows C for cylinders
and agrees with Eshbach. It also extends the graph to Re as low as
0.0001:
Re C
0.0001 20,000
0.001 3,000
0.01 400
Best I can do, offhand.
There may be a C calculator on the web somewhere, but I am at home now
- slow connection.
Tom Davidson
Richmond, VA
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| User: "Andy Resnick" |
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| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 08:48:40 AM |
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Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
Thanks to everyone who answered.
In a frenzy, I recovered the reference:
Am J Physiol. 1997 Jan;272(1 Pt 2):F132-8. "Analysis and modeling of the
primary cilium bending response to fluid shear."
where the formula is given:
'fluid drag on the cilium can be calculated from a standard formula for
laminar flow around a cylindrical object f =
(4*pi*rho*v^2*d)/(Re[2.002-ln(Re)]), where rho is the fluid density, v
the velocity, d the diameter of the cylinder, and Re the Reynolds number'
They refer to Tritton's "Physical Fluid Mechanics", which I need to get,
apparently.
Here's the reason why I care- I'm currently studying nonmotile cilia,
but motile cilia are looming large, and the main issue is the
fluid-cilium interaction: how motion of the fluid is coupled to either
deflection or motion of cilium (or flagellum). There's tons of
theoretical work, and there's some experimental work, but there is zero
coupling between the two, to compare competing theories, for example.
Thanks again!
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
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| User: "cnctut" |
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| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 03:48:43 PM |
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Andy Resnick wrote:
Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
Thanks to everyone who answered.
In a frenzy, I recovered the reference:
Am J Physiol. 1997 Jan;272(1 Pt 2):F132-8. "Analysis and modeling of the
primary cilium bending response to fluid shear."
where the formula is given:
'fluid drag on the cilium can be calculated from a standard formula for
laminar flow around a cylindrical object f =
(4*pi*rho*v^2*d)/(Re[2.002-ln(Re)]), where rho is the fluid density, v
the velocity, d the diameter of the cylinder, and Re the Reynolds number'
They refer to Tritton's "Physical Fluid Mechanics", which I need to get,
apparently.
Here's the reason why I care- I'm currently studying nonmotile cilia,
but motile cilia are looming large, and the main issue is the
fluid-cilium interaction: how motion of the fluid is coupled to either
deflection or motion of cilium (or flagellum). There's tons of
theoretical work, and there's some experimental work, but there is zero
coupling between the two, to compare competing theories, for example.
Thanks again!
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
//
Andy,
If you don't mind, what is the range of Reynolds numbers your equation
is good for?
Thanks,
Tut
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| User: "Sorcerer" |
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| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 05:36:33 PM |
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|
"cnctut" <cnctutwiler@wmconnect.com> wrote in message
news:1156366123.923466.66350@p79g2000cwp.googlegroups.com...
|
| Andy Resnick wrote:
| > Andy Resnick wrote:
| >
| > > I misplaced a reference paper that had an equation for the fluid drag
| > > force per unit length of a cylinder, flow perpendicular to the
cylinder
| > > axis. It was was for low Reynolds number, and all I can remember is a
| > > factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
| > > Sound familiar?
| > >
| > > Can someone provide a hint?
| >
| > Thanks to everyone who answered.
| >
| > In a frenzy, I recovered the reference:
| >
| > Am J Physiol. 1997 Jan;272(1 Pt 2):F132-8. "Analysis and modeling of the
| > primary cilium bending response to fluid shear."
| >
| > where the formula is given:
| >
| > 'fluid drag on the cilium can be calculated from a standard formula for
| > laminar flow around a cylindrical object f =
| > (4*pi*rho*v^2*d)/(Re[2.002-ln(Re)]), where rho is the fluid density, v
| > the velocity, d the diameter of the cylinder, and Re the Reynolds
number'
| >
| > They refer to Tritton's "Physical Fluid Mechanics", which I need to get,
| > apparently.
| >
| > Here's the reason why I care- I'm currently studying nonmotile cilia,
| > but motile cilia are looming large, and the main issue is the
| > fluid-cilium interaction: how motion of the fluid is coupled to either
| > deflection or motion of cilium (or flagellum). There's tons of
| > theoretical work, and there's some experimental work, but there is zero
| > coupling between the two, to compare competing theories, for example.
| >
| > Thanks again!
| >
| > --
| > Andrew Resnick, Ph.D.
| > Department of Physiology and Biophysics
| > Case Western Reserve University
| //
|
|
| Andy,
|
| If you don't mind, what is the range of Reynolds numbers your equation
| is good for?
What do you care? You have no interest in math or physics, Toot.
I'm busy trying to imagine you with a personality. Maybe you'd be less
boring once I got to know you, but I don't want to take that chance. Why
don't you close your mouth before someone sticks an apple in it? Maybe you
wouldn't be such a Jerk-In-The-Box if you weren't so dumb that even blondes
tell jokes about you.
Androcles
.
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| User: "cnctut" |
|
| Title: Re: Q: drag force on a cylinder |
23 Aug 2006 06:22:53 PM |
|
|
Sorcerer wrote:
"cnctut" <cnctutwiler@wmconnect.com> wrote in message
news:1156366123.923466.66350@p79g2000cwp.googlegroups.com...
|
| Andy Resnick wrote:
| > Andy Resnick wrote:
| >
| > > I misplaced a reference paper that had an equation for the fluid drag
| > > force per unit length of a cylinder, flow perpendicular to the
cylinder
| > > axis. It was was for low Reynolds number, and all I can remember is a
| > > factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
| > > Sound familiar?
| > >
| > > Can someone provide a hint?
| >
| > Thanks to everyone who answered.
| >
| > In a frenzy, I recovered the reference:
| >
| > Am J Physiol. 1997 Jan;272(1 Pt 2):F132-8. "Analysis and modeling of the
| > primary cilium bending response to fluid shear."
| >
| > where the formula is given:
| >
| > 'fluid drag on the cilium can be calculated from a standard formula for
| > laminar flow around a cylindrical object f =
| > (4*pi*rho*v^2*d)/(Re[2.002-ln(Re)]), where rho is the fluid density, v
| > the velocity, d the diameter of the cylinder, and Re the Reynolds
number'
| >
| > They refer to Tritton's "Physical Fluid Mechanics", which I need to get,
| > apparently.
| >
| > Here's the reason why I care- I'm currently studying nonmotile cilia,
| > but motile cilia are looming large, and the main issue is the
| > fluid-cilium interaction: how motion of the fluid is coupled to either
| > deflection or motion of cilium (or flagellum). There's tons of
| > theoretical work, and there's some experimental work, but there is zero
| > coupling between the two, to compare competing theories, for example.
| >
| > Thanks again!
| >
| > --
| > Andrew Resnick, Ph.D.
| > Department of Physiology and Biophysics
| > Case Western Reserve University
| //
|
|
| Andy,
|
| If you don't mind, what is the range of Reynolds numbers your equation
| is good for?
What do you care? You have no interest in math or physics, Toot.
I'm busy trying to imagine you with a personality. Maybe you'd be less
boring once I got to know you, but I don't want to take that chance. Why
don't you close your mouth before someone sticks an apple in it? Maybe you
wouldn't be such a Jerk-In-The-Box if you weren't so dumb that even blondes
tell jokes about you.
Androcles
Tut writes:
Shigella (Androcles),
I thought I might take a crack at deriving the formula, if the OP sets
boundaries on the Reynolds numbers.
Should I have asked your permission first--grasshopper?
Tut
.
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| User: "Sorcerer" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 02:46:41 AM |
|
|
"cnctut" <cnctutwiler@wmconnect.com> wrote in message
news:1156375373.337704.107160@m73g2000cwd.googlegroups.com...
|
| Sorcerer wrote:
| > "cnctut" <cnctutwiler@wmconnect.com> wrote in message
| > news:1156366123.923466.66350@p79g2000cwp.googlegroups.com...
| > |
| > | Andy Resnick wrote:
| > | > Andy Resnick wrote:
| > | >
| > | > > I misplaced a reference paper that had an equation for the fluid
drag
| > | > > force per unit length of a cylinder, flow perpendicular to the
| > cylinder
| > | > > axis. It was was for low Reynolds number, and all I can remember
is a
| > | > > factor of something like 'Re*sqrt[2.02- ln(Re)]' in the
denominator.
| > | > > Sound familiar?
| > | > >
| > | > > Can someone provide a hint?
| > | >
| > | > Thanks to everyone who answered.
| > | >
| > | > In a frenzy, I recovered the reference:
| > | >
| > | > Am J Physiol. 1997 Jan;272(1 Pt 2):F132-8. "Analysis and modeling of
the
| > | > primary cilium bending response to fluid shear."
| > | >
| > | > where the formula is given:
| > | >
| > | > 'fluid drag on the cilium can be calculated from a standard formula
for
| > | > laminar flow around a cylindrical object f =
| > | > (4*pi*rho*v^2*d)/(Re[2.002-ln(Re)]), where rho is the fluid density,
v
| > | > the velocity, d the diameter of the cylinder, and Re the Reynolds
| > number'
| > | >
| > | > They refer to Tritton's "Physical Fluid Mechanics", which I need to
get,
| > | > apparently.
| > | >
| > | > Here's the reason why I care- I'm currently studying nonmotile
cilia,
| > | > but motile cilia are looming large, and the main issue is the
| > | > fluid-cilium interaction: how motion of the fluid is coupled to
either
| > | > deflection or motion of cilium (or flagellum). There's tons of
| > | > theoretical work, and there's some experimental work, but there is
zero
| > | > coupling between the two, to compare competing theories, for
example.
| > | >
| > | > Thanks again!
| > | >
| > | > --
| > | > Andrew Resnick, Ph.D.
| > | > Department of Physiology and Biophysics
| > | > Case Western Reserve University
| > | //
| > |
| > |
| > | Andy,
| > |
| > | If you don't mind, what is the range of Reynolds numbers your equation
| > | is good for?
| >
| > What do you care? You have no interest in math or physics, Toot.
| >
| > I'm busy trying to imagine you with a personality. Maybe you'd be less
| > boring once I got to know you, but I don't want to take that chance. Why
| > don't you close your mouth before someone sticks an apple in it? Maybe
you
| > wouldn't be such a Jerk-In-The-Box if you weren't so dumb that even
blondes
| > tell jokes about you.
| > Androcles
|
| Tut writes:
|
| Shigella (Androcles),
|
| I thought I might take a crack at deriving the formula, if the OP sets
| boundaries on the Reynolds numbers.
|
| Should I have asked your permission first--grasshopper?
|
| Tut
Do as you wish, but you have displayed no interest in physics or math
and a clear interest in trolling.
I'm not carrying your math books for you, even if you can find the
difference between R and 1/R you still haven't a clue what a constant
velocity is, slug.
Androcles
.
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| User: "Andy Resnick" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 08:24:47 AM |
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cnctut wrote:
<snip>
Andy,
If you don't mind, what is the range of Reynolds numbers your equation
is good for?
That's a really good question! I have no idea, that's why I ordered
Tirtton's book- I want to see how that expression was derived.
For my system, the Reynolds number is < 10^-6 or so. But the surfaces
are not smooth.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
|
|
|
| User: "cnctut" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 03:24:54 PM |
|
|
Andy Resnick wrote:
cnctut wrote:
<snip>
Andy,
If you don't mind, what is the range of Reynolds numbers your equation
is good for?
That's a really good question! I have no idea, that's why I ordered
Tirtton's book- I want to see how that expression was derived.
For my system, the Reynolds number is < 10^-6 or so. But the surfaces
are not smooth.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Andy,
Thanks for the reply--now I understand your problem -- Ren < 10 ^ -6 is
pretty small. The only cylinder data I have is for Cd's down to around
Ren = 6. The Cd vs Ren looks pretty straight for Ren 6 to about 150--
and as Tadchem pointed out, Stokes is a bust.:-(
VR
Tut
.
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| User: "tadchem" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 04:36:13 PM |
|
|
Andy Resnick wrote:
Here's the reason why I care- I'm currently studying nonmotile cilia,
but motile cilia are looming large, and the main issue is the
fluid-cilium interaction: how motion of the fluid is coupled to either
deflection or motion of cilium (or flagellum). There's tons of
theoretical work, and there's some experimental work, but there is zero
coupling between the two, to compare competing theories, for example.
You have quite a job set for yourself. The difference between
non-motile and motile cilia ia directly comparable to the difference
between the aerodynamics of fixed-wing aircraft and that of birds, or
between laminar and turbulent flow.
You can expect some computationally intensive analyses.
Best of luck, and thanks for the news updates.
Tom Davidson
Richmond, VA
.
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| User: "" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 04:26:11 AM |
|
|
In article <echm81$k2o$1@eeyore.INS.cwru.edu>,
Andy Resnick <andy.resnick@op.case.edu> wrote:
Andy Resnick wrote:
I misplaced a reference paper that had an equation for the fluid drag
force per unit length of a cylinder, flow perpendicular to the cylinder
axis. It was was for low Reynolds number, and all I can remember is a
factor of something like 'Re*sqrt[2.02- ln(Re)]' in the denominator.
Sound familiar?
Can someone provide a hint?
Thanks to everyone who answered.
In a frenzy, I recovered the reference:
Am J Physiol. 1997 Jan;272(1 Pt 2):F132-8. "Analysis and modeling of the
primary cilium bending response to fluid shear."
where the formula is given:
'fluid drag on the cilium can be calculated from a standard formula for
laminar flow around a cylindrical object f =
(4*pi*rho*v^2*d)/(Re[2.002-ln(Re)]), where rho is the fluid density, v
the velocity, d the diameter of the cylinder, and Re the Reynolds number'
Wow. You'ld never guess that a cilium would know that math ;-).
They refer to Tritton's "Physical Fluid Mechanics", which I need to get,
apparently.
Here's the reason why I care- I'm currently studying nonmotile cilia,
but motile cilia are looming large, and the main issue is the
fluid-cilium interaction: how motion of the fluid is coupled to either
deflection or motion of cilium (or flagellum). There's tons of
theoretical work, and there's some experimental work, but there is zero
coupling between the two, to compare competing theories, for example.
Thanks again!
Whoa. How in the world...? I sure would like to watch how
you set up a lab.
/BAH
.
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|
| User: "Andy Resnick" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 08:27:03 AM |
|
|
wrote:
<snip>
Whoa. How in the world...? I sure would like to watch how
you set up a lab.
Well, if you ever find yourself in Cleveburg, I'll be happy to show you
around.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
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|
| User: "Sorcerer" |
|
| Title: Re: Q: drag force on a cylinder |
24 Aug 2006 09:11:45 AM |
|
|
"Andy Resnick" <andy.resnick@op.case.edu> wrote in message
news:eck9b8$2av$2@eeyore.INS.cwru.edu...
| wrote:
|
| <snip>
| >
| > Whoa. How in the world...? I sure would like to watch how
| > you set up a lab.
|
| Well, if you ever find yourself in Cleveburg, I'll be happy to show you
| around.
Is that the Cleveburg near Springfield?
Androcles
.
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| User: "" |
|
| Title: Re: Q: drag force on a cylinder |
27 Aug 2006 05:15:21 AM |
|
|
In article <eck9b8$2av$2@eeyore.INS.cwru.edu>,
Andy Resnick <andy.resnick@op.case.edu> wrote:
jmfbahciv@aol.com wrote:
<snip>
Whoa. How in the world...? I sure would like to watch how
you set up a lab.
Well, if you ever find yourself in Cleveburg, I'll be happy to show you
around.
Thanks :-). I was thinking of being a fly on the wall, or rather
since you're studying cilia, a paramecium to watch how you
study this stuff. If I'm there as a human, you wouldn't be
working.
/BAH
.
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