Calculating flow through branch piping

[shup0739]

I have a 2" shd 40 pipe running horizontal for about 2 ft and then takes a 90 deg turn and heads for about 2 ft where it breaks into a T-Connection and goes left and right. My question, if I konw what the flow at the start which is 112 how do I figure my flow at the T-connection to the right and left side.

I know I have to figure out K-values from friction fitting loss. I can figure out the head loss in ft with the following formula H=kV^2/2g up until the pipe takes that 90 bend but I don't know how to figure the flow at that bend or after that bend. I know that my flow will be reducing as I take turns and bends due to friction and fitting loss, I would really appreciate if someone can guide me on how to calculate the flow or how to use these fitting loss tables to find the final flow.

 

[TD2K]

Fitting losses are usually calculated in terms of equivalent feet. For example, the L/D for a LR welded elbow is 14. Since 2" sch 40 pipe ID is 2.067", the equivalent length is 28.94" or 2.4 feet and you can calculate the pressure drop from that.

The tee is trickier. If the flow splits at the tee and parts goes one way and part goes the other way, as it sounds like, it's a trial and error solution possibly.

You need to look at the piping attached to each 'outlet' of the tee. If the piping downstream of the tee is long then you can assume the pressure drop across the tee is minor and ignore it. You essentially know the pressure at the inlet to the tee and 2 lengths of pipe leaving the tee to some final destination pressure. That's going to be a trial and error solution to find out how the flow splits to satisfy your hydraulics.

If you have to include the relative pressure drop across the tee, the only reference I have is "Mechanical Design of Process Systems", 2nd edition. They have fitting losses where the flow splits across a tee or different angled fittings.

 

[shup0739]

Yes I understand how to figure out the head loss calculations but How do I then find the flow of water in the pipe downstream.

The piping down stream is identical in size and orientation and therefore I would assume that the flow at the T-connection would be equal since the piping scheme downstream is identical in size. Moreover, if I figure out the total head loss in ft just before the T-connection, how do i then use this info to find my flow of water in GPM.


thank you in advance

 

[BobPE]

Do the pipes connect again downstream? If so, use the hardy cross formula. If not, then merely figure out the hydraulic gradient at the point of discharge.

BobPE

 

[TD2K]

Well, you said "... the pipe takes that 90 bend but I don't know how to figure the flow at that bend or after that bend" so I gathered from that you didn't know how to calculate the pressure drop across the 90 degree elbow.

You also said "I know that my flow will be reducing as I take turns and bends due to friction and fitting loss". I'm assuming this is a liquid system since you are using H=kV^2/2g (although technically, you can do this for a gas). For a liquid, the flow does not change as the pressure decreases because you still have to conserve mass in the system.

Anyway, back to what I think is your question. If the piping is symetrical downstream of the tee and both runs are the same size and both runs go to the same final source pressure, the flow will split 50/50.

You said in your first post the flow at the starting point is 112 in your units. The sum of the flow through both legs after the tee then has to be 112. So, if both legs are symetrical and goes to the same final delivery pressure, the flow in each leg is 56 in whatever units you are using. To determine the starting pressure, you'll need to work backwards from your final delivery points back up the piping.

 

[sudhir2021]

Dear Shup0739,
I presume you are mixing two things (flow & head loss) and confusing. U said "I know that my flow will be reducing as I take turns and bends due to friction and fitting loss".....well flow in the pipe line will not reduce due to bends and Tee. Bends, Tees & pipe length will result in head loss (i.e. pressure drop in pipe line). Second thing is" how to calculate the flow after T-connection), well it basically depends on your end discharge & starting flow condition. If I assume that all ur diversion are on a horizontal plane and the Tee split the incoming pipe into two direction of equal diameter than ur flow in each pipe will be half of ncoming flow i.e. 56.
At any jt. of pipe flow: SUM (Discharge)=0
i.e. SUM (Qin) = SUM (Qout)
in ur case at T-connection,
Qin = 112 = Qout1+Qout2
as diameter of both outgoing pipe is equal and the end discharge conditions are same,
so Qout1 = Qout2 = Qin/2= 56

Again if U want to calculate the head loss in the piping network, same can be done by
Head loss = Major head loss + Minor Head loss
Major Head loss is the head loss that will occur in the straight length of pipe due to friction and can be calculated by Hazen Willium or Darcy Weisback formula. If u consider Hazen-Willium formula:
Major Head loss in pipe
hf= ((149 x Q)/(C x D^2.63))^1.85
where: hf=head loss in feer per 1000 ft; Q= flow in pipe in gallons per minute; D= pipe diameter in inches;C= HW coefficient = 150 for PVC/HDPE, 140 for cement lined pipe, 100 for CI/DI pipe, 120 for steel pipe
Minor loss is the head loss that will occur in the pipe at bends, tess etc. minor head loss at bends etc can be calculated by K x V^2/2g
where K = 0.075 for 22.5 deg bend, 0.10 for 30 deg, 0.2 for 45 deg, 0.35 for 60 deg, 0.8 for 90 deg bend (miltered), 0.75 for Tee branch flow.

 

[shup0739]

Thank you all for your replies. You have really helped me tremendously.

Yes I am confusing flow with head loss. I appologize for that. Moreover, it makes sense that the amound of water that I begin with must not decrease because of the conservation laws. If I have 112 GPM on the main header and this splits into 2 and and off of these two secondary pipes each break into 4 branches then the sum of all 8 branches should equal 112 GPM.

Yes my primary T connection is on a horizontal plane however after this diversion the piping schem on both sides goes vertically upwards and then horizontally into the vessel.

I guess the question or my question is if I know that the flow will split 50/50 at the T connection and I have 4 branches off of the T-connection how will the distribution of flow be at the four branches after the T.

Can I simply us Fluid Mechanics
Conservation of Mass formula
m dot in = m dot out


But yeah the head loss refers to pressure calculations which I was getting confused on.

thanks

 

[TD2K]

IF the piping downstream of the tee is the same size AND symetrical and IF the water level in the tanks are the same elevation to each other, then the flow will split 50/50.

If that isn't true, more water will flow down the hydraulically 'shorter' leg (due either due to piping length, piping size or the tanks' water level/elevation).

To determine the flow down each leg, it's a trial and error solution working back from each tank along the piping to the inlet of the tee changing the flow rate down each leg until the inlet pressure to both legs are the same AND the total flow rate is 112 units.

Set up a spreadsheet, you'll go nuts doing this by hand.