Effect on flow after sudden expansion

[shripadgb]

Hi everybody,

My query is regarding "the effect of flow rate due to sudden expansion in a pipeline keeping the inlet and out let conditions constant i.e. no pump or turbine in the pipeline"

There is a 50NB (mm, Nominal Bore) tapping in a 150 NB water pipeline and this 50 NB pipeline extend upto the underground tank which is approx. 100 mtrs from the tapping. i.e. the lengh of 50 NB pipe is 100 mtrs. With is arrangement, we are getting, say Q1 flow in the underground tank and the tank is getting 50% filled. Now we want to increase the flow. Hence, we want to do the following modification in the line 50 NB pipeline. We are planning to provide a expander (50 NB x 80 NB) at a distance of approx. 200 mm from the header tapping and will extend the 80 NB upto the underground tank. The entry point of pipe in the underground tank is at the top.
Now, my question is, by doing this modification, whether there is any increase in flow of water so that the u/g tank will get filled with more water?
(Please note that the pressure in the main header (150 NB) is constant and at the end of 80 NB line is also atmospheric pressure.)
I have attached a schematic diagram of the proposed modification for ready reference

Regards,
Shri

 

[lpfr]

You can compute the flow rate in the pipes (the 200 mm one and the 100 meters one) with the abacus published in this site: http://www.fristam.de/pdf/2uk.pdf
Of course, there will be some differences with reality because the flow and the loss of head at the junctions is hard to model.

 

[Q_Goest]

Hi shrip,
Welcome to the board.

Now, my question is, by doing this modification, whether there is any increase in flow of water so that the u/g tank will get filled with more water?

There will be an increase in flow rate, but the level at which the water will rise won't change. I think you're only asking about flow rate though, not level in the tank, is that right?

If you'd like an example of how to calculate flow through a pipe, check the examples I posted here:
https://www.physicsforums.com/showthread.php?t=161862

To determine the added restriction of a sudden expansion, you can use the resistance coefficient given in Crane paper #410, which any engineer doing pipe flow should have a copy of. You can also find that information outlined for sudden and gradual expansions here:
Sudden:
http://www.mathworks.com/access/hel...lbox/physmod/hydro/ref/gradualareachange.html

Gradual:
http://www.mathworks.com/access/hel...sudden+expansion+resistance+coefficient+crane

Note that there's also an entrance and exit loss associated with the system you show.

 

[quark]

There are two non practical assumptions here. One is that there is no pump in the system. Second one is that pressure in the header remains constant. I don't have issues (if mods forgive me) as long as this is a homework problem. Otherwise, better description of the system may yield better answer.

As the length of the piping, difference of inlet and outlet pressures (i.e the system pressure drop) are constant and ignoring the different in pipe roughnesses, you can approximately compute the new flowrate by D-W equation. Upon simplification, the ratio of flowrates equals square root of 5th power of diameter ratio. So, your flowrate may tripple, approximately.