Calculating pressure required to flow at desired rate through pipe

[MightyG]

I have a problem which I am working on and its been a while since I did this at uni so I am after a little guidance :)

Im trying to work out what pressure will be required to flow at a specific rate through a piece of pipe, the pipe begins with an ID of approximately 1-1/2" then drops to around 1/4" and I am hoping to pump at around 3-4bbl/min through the 1/4" pipe. (126-168Gal/min)

I was thinking of using bernoulis equation and working out the pressure and velocity in the 1/4" pipe then use that work work out the pressure and velocity in the 1-1/2" pipe at the opening of the 1/4"

from this I can then add on the friction loss through the 1-1/2" to get the total pump pressure to pump through the entire length? (I am ignoring the friction loss through the 1/4" as I assume it will be negligible, its only going to be approximately 6-ft compared to approximately 2000-ft of the 1-1/2")

Am I thinking along the right tracks with this or is there another, better way to work this out?

 

[MightyG]

If I am correct in this line of thought then can I say the pressure of the end of the 1/4" pipe will be the same pressure as the area it is pumping into?

In this instance the 1/4" tubing will be pumping into an area which is pressurised up to 11Kpsi, can I use this as the pressure for one half of the Bernoulli equation and us it to work back to the pressure in the 1-1/2"?

 

[rcgldr]

Bernoulli's equation assumes the pipe does no work against the flow. In real life, friction with the walls of the pipe and viscosity of the fluid reduces pressure of a flowing fluid as the fluid flows down the pipe. The longer the distance, the more reduction there is in pressure, assuming pipe diameter doesn't change. Turbulence at transition points in pipe diameter is also going to affect the pressure. Flow will remain constant throughout the pipe (other than initial start up).

 

[Q_Goest]

As mentioned, Bernoulli's isn't going to provide the irreversible pressure loss through the pipe. Generally, the Darcy Weisbach equation is used to determine this pressure drop. The attachment on https://www.physicsforums.com/showthread.php?t=179830" goes through pipe pressure drop analysis.

 

[schip666!]

Apriori calculating the thing is probably nigh impossible since you need to know all the friction and elevation change components. As a fire-person I'm interested in results so I looked up these tables for you:
http://www.elkhartbrass.com/files/aa/downloads/catalog/catalog-e-T.pdf
Page 8 has a nice table "DISCHARGE OF SMOOTH BORE NOZZLES/TIPS"...

The red flag was wanting to get >100gpm from a 1/4" pipe -- if it was 3/4" I'd say fine, go for it -- of course the above referenced tables are for hoses with nozzles that may restrict the flow a bit, but 'smooth bore' is pretty much exactly what it says.