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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

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> 

> 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
Exeter University

Biological Sciences
Hatherly Laboratories
Prince of Wales Road
Exeter EX4 4PS. UK.

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