flowrates of 1 input 5 output system as a function of pipe diameter.
flowrates of 1 input 5 output system as a function of pipe diameter.
(OP)
I am trying to model a spray nozzle.
There is 1 pressureized stream in of which I know the volumetric flowrate, and 5 streams out to atmosphere of varying Cross sectinal areas.
I need to know the velocities and flowrates of each outlet stream. The fluid is essentially water.
___________________
Qi --->| |-->A1,v1
| |-->A2,v2
| |-->A3,v3
| |-->A4,v4
| |-->A5,v5
|__________________|
I believe the interaction is similar to 5 parallel resistors in an electrical circuit, but I'm not sure how to calculate the equivalent resistance. I'm sure it's inversely proportional to the cross sectional area, but I'm not exactly sure how to do it.
All outlets are at the same height.
It's been 8 years since my last brush with Fluid Dynamics in college. I've had to purge that memory for stuff more related to my field.
Can somebody help?
-Jeremy Foland
There is 1 pressureized stream in of which I know the volumetric flowrate, and 5 streams out to atmosphere of varying Cross sectinal areas.
I need to know the velocities and flowrates of each outlet stream. The fluid is essentially water.
___________________
Qi --->| |-->A1,v1
| |-->A2,v2
| |-->A3,v3
| |-->A4,v4
| |-->A5,v5
|__________________|
I believe the interaction is similar to 5 parallel resistors in an electrical circuit, but I'm not sure how to calculate the equivalent resistance. I'm sure it's inversely proportional to the cross sectional area, but I'm not exactly sure how to do it.
All outlets are at the same height.
It's been 8 years since my last brush with Fluid Dynamics in college. I've had to purge that memory for stuff more related to my field.
Can somebody help?
-Jeremy Foland





RE: flowrates of 1 input 5 output system as a function of pipe diameter.
a formula that shows that square of the flow rate varies with the fifth power of the diameter. Or the flow is proportional
to the 2.5 power of th diameter. So if each branch has the same friction factor and length and outlet pressure (e.g. atmospheric discharge), this would be the case.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
I found a formula for Equivalent pipe resistance, but the variables aren't explained. It was something like (8 pi mu)/A, but that doesn't jive.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
The following site might be of some assistance in your calculations:
http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
Sorry, all. Even though by diploma I am a Chemical Engineer, I'm currently employed in the Electrical field, so I think like an Electrical Engineer (..Gasp!)
You know, I think you are right. The Constant Pressure source is like a constant voltage source, where a constant flowrate system would be like a constant current source.
If I hook ten resistors up to a battery (Assuming I don't load down the system) the current through each resistor obeys Ohms Law. However if there is a constant current, then it gets a little more complicated, and interplay results.
I'm going to try to find a Crane's handbook around here. Otherwise, I'll use that website that ve7brz suggested. Thanks all for your help.
Regards,
Jeremy Foland
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
Could you please give me the complete title and publisher of that Crane's Handbook. I searched Google and just got a handbook about Cranes (Construction machinery :) )
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
http://www.cranevalve.com/tech.htm
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
www.cranevalve.com/tech.htm
BTW, I don't know how REAL "constant" voltage and current sources work, but "rbcoulter" just scratched the surface by pointing out that you might have to take the flow/pressure source into account. A centrifugal pump has a characteristic curve of discharge pressure vs. flow and is therefore not a constant anything. Pos. displ. pumps are fairly close to constant flow. This could be an iterative solution if you must consider significant "turndown" to your system due to changes in total discharge area.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
1. Assume a total flow rate, Q
2. Calculate discharge pressure of pump (from pump curve)
3. Calculate resistances of each pipe branch (from
Crane formula above).
4. Determine flow in each branch.
5. Add all flows in each branch and compare to
Q above.
6. Adjust initial guess of Q and repeat steps above until there is an agreement.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
There is no pump, and the fluid is driven by a nitrogen line on the backside of a buffer tank, and can be considered very stable.
Thanks everyone for all of the help. I've reccomended this site to several of my engineering buddies. I hope I can give as much as I've received!
If I still have problems, I'll post here later.
Thanks again.
BTW, I got ahold of the Crane Book, but can't fine the formula specified. My version was reprinted on 7/96
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
Thanks ve7brz for the websote you suggested.
Using Bernoulli's law
r = Density
g = Gravitational Constant
z = head
P = Pressure
v = velocity
rgz + Pin + 1/2rVline^2 = rgz+Patm+1/2rV1^2
^Negl ^I'll say buffer tank is stagnant and drops
Pin = rgz + 1/2rV1^2 + patm
^ negligible
V1 = (2(Pin-Patm)/r)^0.5
I'm happy with that solution. EXCEPT, everyone keeps asing me the same question.
"When I stick my thumb over the end of a garden hose, the velocity coming out of the hose increases (Shoots farther). Why does your equation suggest that velocity is independent of cross sectional area?!"
And I say....Hmm, I'm not sure.
Does it have something to do with friction loss being less for the turbulent flow which is produced by reducing the reynolds number?
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
"A diverging passage.... should not be modeled using the Bernoulli equation. Adverse pressure gradients cause rapid growth of boundary layers, severely distorted velocity profiles, and POSSIBLE FLOW SEPARATION." ........
"Flow separation that can occur at inlets with sharp corners and in abrupt bends, causes the flow to depart from that predicted by a one-dimensional model and the Bern. eq."
Introduction to Fluid Mechanics
5th Edition
Fox and Mcdonald
page 256
Streamlines must be indentified for use of Bernoulli's, and having a finger over the hose distorts these lines. I think. Correct me if I am wrong.
Roach
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
By putting your thumb over the end of the pipe you slow that water flow down enough in the hose/pipe so that the pressure drop (lost to friction) in the hose is significantly reduced. Now the pressure at the end of the hose/pipe is very close to the inlet pressure of the hose. The result is higher pressure and thus higher velocity from the end of the hose but lower flowrate.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
Air flows are usually a different matter where the velocity term is significant in many cases.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
I think you missed out the continuity equation, which is:
A1V1 = A2V2
where A1 & A2 are the area of pipe before and after reduction, V1 & V2 is the corresponding velocity of fluid.
As a result, when you place your thumb at the hose end, you reduced the area of the pipe (similar to adding a jet nozzle) thus making the velocity increase.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
You're right. The continuity equation applies for the hose because it's a restriction of an existing pipe flow.
Why does it not apply to a Draining tank?
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
I think the continuity equation also applies to draining tank.
However, with a very large surface area of the tank compare with the pipe cross-section area, the velocity in the tank will be very small and will be taken as negligible for ease of calculation. But this does not mean it does not exist at all.
Perhaps you can consider a large hydraulic piston with a very small oil infeed pipe. When oil is feed into the piston, the piston will move very slow, but it still move.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
For example, let's take the hose out of the problem, and imagine a half inch hose punctured at the water supply (where the pressure is constant). As long as there is enough "capacitance" , such as a large water tank, then the velocity coming out of the half inch hole is the same before and after the thumb is applied to the hole.
This is because the pressure does not change upstream of the hole unlike the situation at the end of a long hose where the pressure does change when you apply your thumb.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
The supply pressure (P1) to the pipe is constant.
The pressure at the end of the pipe (P2) (just before the thumb) is not constant. The flowrate Q, does change,
when you apply the thumb. It gets smaller. The pressure behind the thumb gets bigger as you cover up more of outlet area of the pipe/hose.
Look at it this way. The pipe has a definite K value that doesn't change. The applying of the thumb increases the total K value of the pipe/thumb system. The inlet pressure to the pipe is the same. The outlet pressure (after the thumb) does not change. So, the flowrate has to go down. Because of the lower flowrate in the pipe, the delta P in the pipe has to be smaller. This means the pressure just before the thumb has to be higher.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
I think that some simple fluid mechanical concepts are being misapplied in some of these posts. Boundary layers and separated flow occur in real flows, but do not need to be considered here to accurately understand what is going on. For the circumstances described in this thread, continuity ALWAYS "applies". Continuity cannot ever be IMPOSED. If I use my thumb to cover progressively more area until I have blocked it entirely, does anyone believe that the flowrate remains constant until it abruptly goes to zero?
You must be certain that mass flow is constant, and from that circumstance, if it is present, one may then make conclusions based upon A1*V1 = A2*V2
"rbcoulter" is making some good points. You must consider the resistance of the entire fluid circuit.
Back to the spray nozzle arrangement: if the resistance of each of the five "legs" is essentially only the nozzle itself and that the resistance of any supply piping is nil (i.e. there is the same value of pressure feeding each nozzle), then any change in nozzle area will change the flowrate, not the velocity.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
When I filled the bottle up, the trajectories of the water streams were the same.
I'm satisfied now.
Thanks for the help, folks.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
It is tough to comprehend, the tank problem is a classic. With the tank, velocity is dependent on the head in the tank. Its related directly tby the fundumental formula used to derive the orifice equation, h=v^2/2g, solve for v and you get the theoretical velocity for any given depth in the tank for any size hole (theorietically!!) Flow is entering the system and need not be conserved and as such becomes a function of the hole size.
That said, now add energy gradients and hydraulic gradients to address energy losses by entrances, exits and friction. You can get an increase from observed velocity by modifying conditions at the discharge that alter the HGL's and make the observed velocity approach the theoritical velocity, determined by pressure, like was discussed before in the hose problem, which is also a classic. The hose must be looked at as a tube when connected to a static source of pressure which has pressure loss unlike an orifice that has entrance and exit.
It is fun to think about....
BobPE
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
you knew how to insert the face the whole time without ever knowing you knew!!!!!!!
Isn't is scary being an engineer at times!!!!!
I don't know of a list, I just use the letters or face punctuation to make them....
Take care
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
RE: flowrates of 1 input 5 output system as a function of pipe diameter.
A lot of words for a simple pressure drop problem, just go to:
http://www.pressure-drop-calculator.com/ (freeware)
or, even better:
http://www.pipeflow.co.uk/ (30-day trial)
there you will find software + equations which do the trick ...
Good luck & Happy New Year!