Simple Application of Bernoulli

[Ussuri]

Folks

I am looking at a simple calc to assess the pressure and velocity at the end of a straight length of rising main. But it has been a while since I did this stuff and dont have access to my old textbooks.

I have a 1300m pipe connected to an existing water main and I'm trying to work out what pressure and flow I am likely to see at the opposite end.

I am getting myself tied into knots because its not a free discharge at the downstream and and its not stationary so I cant eliminate the p2 or u2 component of bernoullis directly. I do remember there was some algerbraic manipulation needed but cant remember, and cant seem to figure it out.

Upstream p1 = 4bar, upstream elevation z1 = 90m.

Downstream elevation is 115m so in this case, assuming no flow or head loss then p2 is about 1.5bar.

How would I go about calculating the discharge at the downstream point?

Any gentle reminders would be appreciated.

 

[quark]

We use Darcy-Weisbach equation to check the flow. Since, available pressure is 1.5 bar (i.e 4-2.5), the maximum flowrate will correspond the flow rate at which 1.5 bar drop happens. So, LHS of D-W equation is 15 (in meters). Calculate 'f', L and d(in meters) are known to you.

 

[zdas04]

D'Arcy-Weisbach is a much better choice of equation than Bernoulli. When Daniel Bernoulli developed his equation he had a long list of simplifying assumptions. A 1300 m pipe would violate many of them.

David

 

[Ussuri]

Ok folks. Thanks for the input. Most appreciated.

 

[waterpipe]

Ussuri: could you please put an sketch of your problem? This definitely helps to give a more proper respond. I am not sure if I've understood this properly: "its not a free discharge at the downstream and and its not stationary".
You might find it useful to look here:

http://www.eng-tips.com/viewthread.cfm?qid=283070

 

[Ussuri]

Waterpipe. I think I'm good thanks. I think I was confusing myself because the point I was looking at was an intermediate length along the pipe so p2 and u2 were unknown. However looking further downstream there are valves at which I have assumed to be my revised '2' location. So with the valve shut u2 = 0 and with the valve open p2 = atm.

Its been a while.