Pressure drop problem (using the darcy law)

[sifr]

Homework Statement

Estimate the pressure drop in a tower packed with porous support. This tower is an integral part of a water oxygenation system and will need to operate over extended periods without cleaning.

From the following data estimate the pressure drop you expect to see on start-up

Diamter = 1.5m
Height = 3m
Support size = 0.004m

Homework Equations

Δp = (uμh)/β

u is liquid velocity
μ is liquid viscosity (I.e. water)
β is bead permitivitty (I.e the support)

The Attempt at a Solution

I have had no problem calculating β and got 4.9 x 10^-9m
Where I get stuck is finding 'u'

for these problems I usually use the formula u = Q/A
Volumetric flow rate over cross sectional area - however in this instance there is no information about the volumetric flow rate

Should I assume a volumetric flow rate? Or is there a way to calculate it from the above information? (sometimes they give something away in the wording such as 'start up' - not sure what I should take from that)

Are there any other equations I can use? This is a 15 mark question so I'm assuming there's a bit of calculation that needs to go into it.

 

[KataKoniK]

Hello,

Thank you for your post. Estimating the pressure drop in a tower packed with porous support is a complex problem that requires careful consideration of various factors. In this case, the most important factors to consider are the liquid velocity, liquid viscosity, and bead permeability.

To start, you can make an assumption about the volumetric flow rate based on the information given. Since the tower is an integral part of a water oxygenation system, it is safe to assume that the volumetric flow rate will be relatively high. You can also consider the fact that the tower will need to operate over extended periods without cleaning, meaning that the flow rate may decrease over time due to clogging.

Once you have an assumption for the volumetric flow rate, you can use the formula u = Q/A to calculate the liquid velocity. Keep in mind that this is an estimate and the actual flow rate and velocity may vary.

Another equation you can use is the Darcy-Weisbach equation, which takes into account the friction factor and the length of the packed tower. This equation may provide a more accurate estimate of the pressure drop in the tower.

Additionally, you can also consider the effects of gravity and buoyancy on the flow within the tower. These may also contribute to the pressure drop and should be taken into account in your calculations.

In conclusion, estimating the pressure drop in a tower packed with porous support requires a combination of assumptions and equations. It is important to carefully consider all relevant factors and make reasonable assumptions to come up with a realistic estimate. I hope this helps. Good luck with your calculations!