Designing an orifice plate to restrict flow 1

[JasonG]

I have designed an underground flow diffuser to recieve bleed off water from a cooling tower. I must restrict the flow of water to the diffuser to less than about 3 gallons per minute. I want to use an orifice plate to do this.

The bleed line is tied into a pressurized pipe. The pressure at the tie in location is 7 psi. The water will be piped through 3/8" vertical copper pipe for a few feet to a 1" horizontal PVC pipe. The PVC drains to the underground flow diffuser.

1. What procedure do I follow to size the orifice?

2. How do I check the velocity at the PVC pipe? I want to make sure that I don't have a jet of water that will damage the pipe or the flow diffuser.

 

[dickon17]

You probably do not need an orifice plate. For 3 usgpm down a 3/8 diameter copper pipe the friction loss is about 94 psi per 100 ft, or approximately 1.0 psi per foot. So, all you need to regulate a flow of 3 gpm out of a 7psi header is about 7 feet of 3/8 open ended copper pipe. To measure the flow use a 5 gallon pail and a stop watch. A ball valve also could be fitted in this line for fine flow adjustment. I assume there are no sophisticated piping regulations to meet?

 

[JasonG]

You are right. My original design did restrict the flow with the friction loss of the pipe length. The owner has asked for an orifice plate for maintenance reasons though.

I can't use a valve for this application either. The restriction needs to be "hard wired" so to speak. I can't take the risk that the valve will be fully opened by an unknowning technician.

 

[dickon17]

The valve would be fully open at the 3 gpm flow rate. The valve is there primarily to stop the flow for maintenance purposes.

However, to keep the owner happy, you would need about a 0.20 inch diam (5mm) orifice plate to get your 3 gpm flow rate.

 

[JasonG]

I see what you mean. Yes, there will be a valve for that purpouse.

Would you mind describing how you arrived at the 0.2 inch diameter?

 

[dickon17]

Classic formula is Q = 19.65 x d2 x C x root head loss.

Q in gpm, d in inches, head loss in feet of water and C is flow coefficient (usually close to 1.0).

In this case head loss (7 psi) is 16 feet. Solving for d2 gives about 0.2 inches.

 

[JasonG]

It looks like that is a derivation of the equation for flow from a tank: Q=C x A x root (2 x g x h) That was what I had planned to use but I wasn't sure if it was appropriate for this application. Thanks for the confirmation I appreciate it.

 

[JasonG]

Thanks for all of your help. I have 2 more questions if you don't mind.

1) Perhaps you can explain something to me that I can't seem to wrap my mind around. It seems common sense that a small hole in an orifice plate will limit the flow through a pipe system. However, the continuity equation states that the flow rate, Q, is the same everywhere in the
pipe. How does the theory reconcile with common sense?


2)The flow will go through the orifice plate and then the vertical 3/8" copper pipe. Will the friction loss in the 3/8" pipe further restrict the flow or does the orifice control?

 

[dickon17]

The flow rate has to be exactly the same, however, as the cross section area reduces, the velocity increases to compensate.

Friction loss in the 3/8 pipe will still be there and must be accounted for, whether or not you have fitted an orifice plate.

 

[mbeychok]

JasonG:

Just to expand on what dickon17 has told you. Perhaps you think that "flow rate" and "velocity" mean the same thing ... they do not.

"Flow rate" means either volume/(unit of time) or mass/(unit of time). For example, either ft³/s or m³/s or lb/s or kg/s.

"Velocity" means linear velocity. For example, ft/s or m/s.

Does that help you understand that the linear velocity increases as the fluid flows through the orifice ... even though the flow rate remains constant?

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[JasonG]

I understand the difference and relationship between flow rate and velocity. I know that if the flow rate is constant then velocity increases with a decrease in area.

So then how is it that an orifice restricts the flow rate? Wouldn't the velocity increase hence maintaining the flow rate?

This is where the formula posted by dickon17 doesn't jive with A1V1=A2V2. I know they are both valid equations but how can they coexist?

 

[dickon17]

When liquids flow in a closed system, exactly how much flow will be created is determined by the balance of two opposing forces. There is the pressure existing in the system (from a pump or a static head) and the discharge pipeline friction loss (which increases with the increase in flow). These two forces will usually find their own balance point.

An orifice will restrict flow by creating a significant increase in friction loss into the discharge system. If the system pressure creating the flow remains the same, and friction increases in the discharge pipeline, then the flow will reduce. This is of course a hugely simplified explanation.

The formula comes from ancient published data, Crane (Chapter 3), page 3-5, "flow through nozzles and orifices". There are many such formulae, each specific to the units being used. I just picked the most convenient one. Flow through the orifice is complex and will vary with the Reynolds number and whether the orifice is sharp edged or not. However, this is not rocket science and I used the simplest formula, since we are not looking for answers to the nearest 5 decimal places.

 

[mbeychok]

JasonG:

With all due respect, it appears (at least to me) that you are unfamiliar with the Venturi effect and the Bernoulli Theorem. I strongly suggest the you read this article:

http://en.wikipedia.org/wiki/Orifice_plate

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[JasonG]

Dickon17 - thank you, thank you, thank you for the explanation. Putting it that way clears it up for me after all these years! Once the flow is in the pipe the flow rate is constant. However, the head loss in the pipe restricts how much flow can ENTER the pipe to begin with.

mbeychok - thanks for the link. I am familiar with those concepts and formulas. I like to be able to visualize the theories so that I can really understand the numbers and equations that I am working with. I am much more familar with open channel flow which is just similar enough to throw me off when working with pressurized systems.

I think I'm good now. Thank you both for your help.