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# ml/min into mm/s

paul stoodley P.Stoodley at exeter.ac.uk
Wed Jul 22 07:54:13 EST 1998

```Sarah,
You have flow rate and want to convert it to a flow
velocity, average flow velocity to be correct. The flow
rate will be the same throughout the pipe line regardless
of geometry but the flow velocity will not. What you need
to do is measure (if the geometry is simple) or guestimate
(if the geometry is complex) the cross sectional area of
the component in the system where you want the flow
velocity, I guess it will be the flow cell. Then divide the
flow rate by the cross sectional area making sure your
units are compatible. 1 ml can be taken as 1 cm^3 for water
(assuming a density of 1000 kg/m^3), which most people do
for reasonably dilute media. I am not sure what you mean by
"0.2mm/sec as a usual speed". The flow velocity will be very
different in different systems, for example in water
distribution systems and heat exchangers you might expect
0.2 - 3 m/s. Since the flow velocity and reactor geometry
determine the shear and mixing in a flow cell you should use
a comparable flow to the system you are trying to model. To
do this you can use the Reynolds number (although there are
other parameters that may be more relevant). The Reynolds
number is the ratio between the inertial forces (density
(rho) * flow velocity (u)) and the viscous forces
(viscosity)(mu). The inertia tends to push the water along
while the viscosity tends to try and stop it.

Re = u * rho * l / mu

l is a characteristic length and is a scaling factor. For a
tube l = the diameter, for a rectangular tube l = 4CSA/WP

CSA = cross sectional area, WP = wetted perimeter = 2
(length * height).

Re can be used as a comparative parameter over a wide range
of flowing systems. Generally flow is laminar below Re 1000
and turbulent above Re 3000.

Hope this helps.

On 21 Jul 1998 08:13:51 -0700 Sarah Boyle <slb7 at ukc.ac.uk>
wrote:

> Dear biofilmers
>
> could anyone provide me with an equation for converting ml/min into
> mm/s; when using a peristalsic pump and a flow cell.
>
> All literature seems to quote 0.2mm/sec as a usual speed, but I am
> uncertain as to how they arrive at this figure when pump speeds are in
> rpm and flow rates are in ml/min.
>
> Surely 0.2mm/s could be highly variable depending on the tube radius?
>
> Help
>
> Sarah Boyle
> Research School of Biosciences
> University of Kent
> CT2 7NJ
>
> 01227 764000 ext. 3023

----------------------
Paul Stoodley

Environmental         Tel: 01392 264348
Microbiology          Fax: 01392 263700
Research              email: p.stoodley at exeter.ac.uk
Group
Exeter University

Biological Sciences
Hatherly Laboratories
Exeter EX4 4PS. UK.

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