Flow through an orifice plate

[84-1074663779]

The flow through a thin sharp edged orifice plate is given by:

Flow in CFM = 13.55 x square root of pressure x diameter in inches squared.

Pressure drop across the orifice being in inches of water.

Here is a worked example of a two inch diameter orifice plate with sixteen inches of measured water pressure drop.

CFM = 13.55 x (square root of 16") x (2" squared)
CFM = 13.55 x 4 x 4
CFM = 216.8

This formula gives very good results, but it assumes that the air upstream of the orifice is completely "dead" undisturbed air.

If the upstream air is highly turbulent, it will not flow so readily through the orifice. A high velocity air stream pointed at the orifice (like with an air hose !) will not give accurate repeatable results either.

A flat, thin sharp edged orifice placed over the test hole of your flow bench will give consistent results where undisturbed room air is drawn unobstructed into the orifice. The same identical orifice fitted into the interior of the bench and used as a measurement orifice, may not perform the same, because the air entering the orifice will most likely be disturbed.

"Thin" and "sharp edged" are relative terms. A three inch hole punched into a piece of sheet metal would be considered thin and sharp edged. A drilled 1/8 inch hole through the same gauge of metal may be neither. The dimensions and hole finish are relative to material thickness. But with care, a suitably thin and sharp edged orifice is not difficult to make in any required size.

*Hint* When drilling an orifice, or boring a hole with a lathe, clamping three sheets of material tightly together, and then using just the middle sheet will usually give excellent results.

[84-1074663779]

Some further thoughts on orifice plates.

If an orifice plate is measuring at fairly low pressure differential, say only one or two inches of water, the hole diameter will be quite large for any given air flow. The air will be passing through it like a Summer breeze, and it will take only a slight amount of up stream turbulence to screw up the flow readings away from the above theoretical orifice flow formula.

On the other hand an orifice plate set up to measure at say ten to twenty inches (or even more) pressure differential, may be only one third the hole diameter (or less). There will be much more violence and fury as the air passes through the orifice plate, and any slight up stream turbulence will have much less effect on the final flow reading accuracy.

When designing an orifice airflow bench, plan on using as high an orifice measurement pressure as your blower will allow. The only disadvantage is that the higher required blower pressure will require more blower power and amps.

Total blower pressure will be cylinder head test pressure plus orifice drop design pressure, and that can end up needing a very large and powerful blower.

A secondary advantage of using relatively high orifice measurement pressures is with the sloping manometer.

Low orifice pressures require a low manometer rise, which suggests an almost horizontal manometer tube. Small errors in leveling the manometer, or slight bends and bows in the tube can significantly effect how far the fluid travels along the tube. This can lead to manometer scale reading errors.

On the other hand, a much higher manometer rise angle, suggests a manometer slope of forty five degrees or even more may be possible.

If you can imagine a vertical flow manometer tube, if it is slightly off vertical, or the tube itself is a bit wavy, it will not effect the fluid level height up the tube to any significant degree. For highest manometer reading accuracy get the manometer slope as steep as possible, it will help to minimise errors in reading the orifice pressure.

The flow manometer traditionally is a sloping manometer, but it does not really need to be sloping. If you can design your flow orifice to generate sufficient pressure, the flow manometer can be made vertical or nearly vertical.

If the flow manometer absolutely must be at a very shallow angle, it may be best to bolt it permanently to a brick wall. If your flow bench is on wheels, and on an uneven floor, the whole flow manometer may require a jacking screw and spirit level to get it back level every time the bench is moved.

[Mouse]

Good job Tony.

One other thing to consider in these orifice equations, is that they also assume there is nothing near the edges of the orifice. Supporting structures that locate the orifice should be well clear of the orifice edge, such as plywood edges, struts, gasket material, etc... An orifice draws a lot of air from it's edges on the inlet side, and the outlet side produces the penomenom called Vena - Contracta. Anything near the inlet edges will disturb the direction of air entry into the orifice, or near the outlet edge of the orifice will disrupt the Vena - Contracta, disturbing the flow characteristics of the orifice.

John

[larrycavan]

I 'll second that motion. Good job Tony!

Larry C

[Mouse]

Oh, and one more thing: Tony's equations assume a standard air density of .075lb/ft^3.

[B. Elliott]

This thread actually answered quite a few questions.

The world is a better place with you guys around.

[84-1074663779]

Very good point John.

Wool tuft testing will quickly demonstrate that most of the flow into an orifice comes in from around the edges. The air flows in radially and then sort of falls over the edge into the hole. Very little air flows in from directly ahead of the orifice, as might be expected intuitively.

That means the orifice plate must be mounted flush on as large an exposed flat surface as can be arranged.

Inside the flow bench, the ideal position for an orifice is right in the centre of one rectangular wall of a very large plenum space, or settling chamber. If the orifice is located very near a wall or a corner (on the upstream side), expect the flow coefficient of the orifice to be changed.

A very good way to test all this, is to fit two identical orifices, fit one directly over the test hole, and the other in the position of the measurement orifice. Ideally there should be identical pressure drops measured across both over a wide range in airflow.

This is difficult to achieve, but if you can get the largest orifice sizes to give equal pressure drops at maximum rated bench airflow, then you know that the measurement orifice corresponds to the above flow formula.

If this can be achieved, then all the smaller sized orifices will fall into line too. Flow and pressure will be entirely predictable over the whole range of orifice diameters. The big one is always the most troublesome to get working.

If measurement orifice flow is "wild" because of turbulence or poor bench internal flow dynamics, different sized orifices will all have unpredictable results and will need individual calibration. If the orifice hole diameters have to be made all sorts of odd sizes relative to each other, that does not inspire confidence in flow bench accuracy.

It is much better to see a nice even progression in flow ranges with a similar even progression in standard inch (or metric) hole diameters. And it is extremely satisfying to be able to rotate your orifice turret to the next flow range, up or down and measure an identical flow figure.

That is the beauty of an orifice flow bench. With a bit of care and some careful testing, accuracy is inherent. It is possible to build an extremely accurate and repeatable bench on a very tight budget.

Whatever you do, don't mount an orifice directly in a pipe, or directly beneath the test hole. Pressure and flow versus orifice diameter will be entirely unpredictable. There is no formula, but each size will need to be individually calibrated. The MercDog bench that everyone copies is a particularly bad example of that design error. The table they give for flow figures versus orifice diameters are all over the place, and so will yours be too. Every bench will be different, definitely not a good way to go about it.

[Mouse]

[larrycavan]

[Greenlight]

Using the parameters given, the 216 cfm you obtained is not so accurate. Using the equation (sorry the subscripts/superscripts don't show up) and converting mass flow to volume flow rate:

mo = (r1 Co Ao Y) / (1 - (Ao/A1)2).5 x (2 (p1 - p2) / r1).5
where: mo is the mass flow rate at the orifice
r is the fluid density
Co is discharge coefficient
A is the area
Y is the compressibility factor
p is the pressure

(the dis. coef. and comp. factors come from the appropriate charts not shown here)

The actual flow should be 205.1 cfm.

[Tony]

The fly in the ointment here, always comes back to knowing the orifice discharge coefficient.

I am sure you are right, but the particular figure that you decide to plug into the formula for the orifice discharge coefficient is going to skew the results.

For most of us here, some simple basis to start off from is better than none at all. The very basic formula offered at the beginning of the thread is suggested as a starting guide only for bench design. But it will get you close.