# Pressure and velocity calculation for microchannel. pls help

• tanvir islam

#### tanvir islam

Me and my friends have been trying (b) for soooo long! we have gone to PhD students and some fluid dynamic doctors for held and they cannot figure this out.

1. Homework Statement

2) This question concerns the design of a ‘micro-chemostat’ device.

E. coli exhibiting chemotaxis can swim up to 20 times its body length per second. Given a chemostat mode fermentation of E. coli in a microbioreactor, with the limiting substrate at a concentration of 0.2 g.l-1, and using the data provided below, answer the following questions:

(a) What is the minimum fluid flow velocity necessary to prevent the E. coli bacteria swimming up the medium supply, and thus contaminating the medium reservoir? Based on this calculate the maximum diameter for the inlet tubing. (Assume that the calculated minimum fluid velocity is the average velocity across the inlet tubing diameter; assume the length of E. coli to be 2 μm).

ANSWER: Velocity = 40um/s and Diameter = 0.784mm

(b) Given a pump capable of providing a maximum applied pressure of 2 atm, can the pump provide sufficient pressure to achieve the fluid velocity required assuming 50 cm inlet tubing? Assume water viscosity. Show your working.

Reactor geometry and experimental set-up:- Inletchannel=30x1x1mm3- Reactor chamber: assume zero flow resistance
- Outletchannel=30x1x1mm3

- Outlet tubing = 10 cm length x 25 μm diameter
- Back-pressure regulator: constant pressure drop of 34 kPa

where μ, D, Q, V are the growth rate, dilution rate, volumetric flow rate and volume of the micro

bioreactor chamber, respectively. Assumption of Monod growth:

where μmax (maximum growth rate) = 1.5 hr , and KS (the ‘half-velocity constant’) = 0.55 g.l , and V (volume of the reactor) = 150 μl.

## Homework Equations

None given (I think we use poisseulle's law)

## The Attempt at a Solution

plug values into poiseulle's law to figure out pressure for each section.
add all the pressures and take away BPR.
ANS: 2atm is not sufficient

attaching and image of my work is not working so I will email you the what i have done if you need it.