Calculation of Velocity and Shear rate in rectangular channel

[Arslan Siddique]

Hi everyone, I would like to know the formula for calculation of velocity and shear rate in my rectangular fluid channel.

Here are the important values regarding my rectangular channel. W= 2.5 mm, H=3 mm, L=35 mm.
Fluid: Diluted Bacterial suspension derived from wastewater.
Flow rate: 0.125 ml/min

Please help me with the calculation of above mentioned parameters.

Thanks for your help.

 

[Chestermiller]

What research have you done on this so far. You do realize that the shear rate at the wall varies around the perimeter of the channel, right?

 

[Arslan Siddique]

Thanks for your reply!

I do understand that shear rate and velocity varies along the perimeter of the channel and it is also location dependent but I would like to assume that it doesn't vary to get an average value of velocity and shear rate.

Can I use the following Formulas for Velocity and shear rate?

V= Q/W*H
Where, V= Velocity, Q= Flow rate, W= Width and H= Height

Y= 8V/D
Where, Y= Shear rate, V= Velocity and D= Diagonal of the rectangular channel

PS: I am doing a simple calculation and don't want to dig deeper into it. I found the above mentioned formulas from google. Do you think that these formulas are correct considering my simple problem?

 

[Chestermiller]

Thanks for your reply!

I do understand that shear rate and velocity varies along the perimeter of the channel and it is also location dependent but I would like to assume that it doesn't vary to get an average value of velocity and shear rate.

Can I use the following Formulas for Velocity and shear rate?

V= Q/W*H
Where, V= Velocity, Q= Flow rate, W= Width and H= Height

Y= 8V/D
Where, Y= Shear rate, V= Velocity and D= Diagonal of the rectangular channel

PS: I am doing a simple calculation and don't want to dig deeper into it. I found the above mentioned formulas from google. Do you think that these formulas are correct considering my simple problem?

You can use the first formula, but not the second. To calculate the average wall shear rate for laminar flow in a duct of odd-ball cross section (including a rectangular duct), see the following reference:
Miller, C., Predicting Non-Newtonian Flow Behavior in ducts of Unusual Cross Section, I&EC Fundamentals, 11, 524-528 (1972)