Possible range of water flow discharge coefficient

[Feldmann359]

Good Morning again

I have an other question regarding the discharge coefficient:
Cd=m./(A0*sqrt(2*rho*DP)) derived from energy and mass conservation formulas:
with
CD=discharge coefficient [/]
m. = mass flow dm/dt [kg/s]
A0 = orifice area [m**2]
rho = water density (function of temp) [kg/m**3]
DP = pressure drop [Pa]

An other definition I found in several textbooks was
Cd=(m. measured/real) / (m. ideal)

m.ideal again calculated from Bernoulli / 1D frictionless
flow.

So the Cd value is a kind of flow efficiency factor. In
textbooks I found values for it in the rage of 0.3 to 0.99.

From my own measurements, I got Cd values of about 1.23.
The measurement object is a sharp edged orifice of approx.
1.5 mm diamter and a water flow rate of approx. 20 to 100 g/s.

My mass flow meters and pressure sensors are all calibrated
and the pressure ports are at the right place.

So, could this be real or did I something wrong?

Thanks in advance for your help!

Stephan

 

[hacksaw]

calculate the reynold's number (based on orifice bore) if it is less than 1500-2000 or so, it could also be higher as it applies only at true equilibrium flow conditions, the flow in laminar and the Cd is proportional to the ratio of heads, above that the square-root relations apply, that is one of the issues involved

the other is that if you have changes in elevation, syphoning can occur and you'll see increased discharge coefficients


also check the flow measurements using timed filling of a container

 

[Feldmann359]

Dear hacksaw,

thanks for your answer. My flow should be fully turbulent, and there is no change in elevation.

 

[hacksaw]

thats good,

to get disch coef > unity then something is either accelerating your flow (conservation of energy) or your d/p measurement is in error, am ignoring bore measurment errors at this point but they can also contribute.

how are you sensing the pressure, how are the impulse leads run, have you satified recommended criteria for static pressure measurements, etc., etc....

 

[hacksaw]

Stephan,

one other factor, how are you establishing the velocity profile at the inlet of you device under test?

If you have a parabolic flow profile the discharge coef is increased relative to the assumed uniform velocity profile

In some cases you can correct for inlet velocity by

1/(1-d^4/D^4) sort of a factor.

 

[Feldmann359]

Dear hacksaw!
Thanks again for your helpful answers. So now I have more time to think about it.
Only a short repetition of your statements to ensure that I undestood you correctly:

1. For laminar flows, Cd = f * P1/P2 ??
2. For turbulent flows : (square root relation?)

I know that for laminar flows, there is a linear relationship between mass flow rate and pressure drop and for turbulent flows, the mass flow is quadratic.

The same is valid for the hydraulic resistance defined as
R.hydraulic = zeta * rho * 0.5 * 1/A**2
where: Zeta : roughness, rho : density, A : orifice diameter.

laminar: delta p = R.hydraulic * Q
turbulent: delta p = R.hydraulic * Q**2
Q: mass flow rate

To the siphoning issue: I have pressure measurent ports
before and after the orifice (at the distance from the orifice as required from an ISO standard - number to be placed here tomorrow) - so even if there would be additional flow energy it would be metered by the flow meter and also the pressure drop would be recorded correctly.

I also agree that bore diameter measurement errors are not very likely. The bores have been optically determined with a measurement microscope.

What do you mean with "impulse leads run" ? The straight
run-in pipe to ensure flow uniformity? It is around 40 * pipe diameter.

What are recommended criterias for static pressure measurements? My sensors have a new calibration, they will
be powered on 30 mins before the measurement, and the
pressure taps are perpendicular towards the flow direction.

Thanks again for your help,
Stephan

 

[hacksaw]

Stephan,

1. the flow is proportional to the sqrt of the meter d/p in turbulent flow- we're saying the same thing, my semantics are at fault

2.static pressure measurements require ports that are burr free, flush with the tube I.D., and as small a diameter as possible. In your case, probably fractions of a mm and filled uniformly. If the pressure taps are comparable to the main run then you are going to have flow induced errors. You cna test the pressure taps if you are able to remove the flow element, at various flow conditions.

3. impulse leads refers to the connection between the pressure taps and the sensor.

4. You have not specified the main pipe size. 40 diameters may not be enough to establish a proper flow profile. The Bernoulli relationships are only valid for uniform velocity profiles. You may need a flow conditioner and upstream run. Calc. the upstream Re number.

For example, if you have swirlor non-uniform velocity profiles in your upstream flow, the apparent Cd will exceed unity

 

[tjkall]

I have a question.
Using PVC pipe , I drilled holes and inserted fittings with a threaded end and a barbed end into the hole in the pipe. The barbed end is on the outside so that I can connect a water manometer to it and the threaded end was fit into the hole. There is no projection of the threaded end into the pipe, it is flush with the inside wall. I then epoxied (epoxyed,used epoxy) the outside of the fitting to the pipe for strength. Does this sound like a reliable means of measuring inline pressure?

 

[GregLamberson]

tjkall

You should start a new thread with your question - hijacking threads is not looked upon with favor.

Greg Lamberson, BS, MBA
Consultant - Upstream Energy
Website:

http://www.oil-gas-consulting.com

 

[Feldmann359]

Dear hacksaw!

The pipe diameter is 5 mm, and 2 mm is the static pressure tap connector - perhaps there is the fault, because the pressure tap bore is too large?
Is there a rule how what pressure tap / pipe diamerter ratios are acceptable?

I will have a look at theses pressure tap bores, I am not sure if they are free of burrs.

But what is a swirlor non-uniform profile? Do you mean it is not free of eddys?

Would you please explain how to use your correction
1/(1-d^4/D^4) ? d=orifice diameter, D=pipe diameter?

Under which circumstances is you correction necessary?

Thanks a lot for your help,
Stephan

 

[hacksaw]

sounds good keep working with it,

the smaller the better, should be in fractions of a mm- the one text still on the shelf shows some data for 0.06" ID taps for different edge shapes. You should be using honed (smoothed) surfaces for elements as small as 2 mm


there is a NASA paper dealing with swirl, lost track of my copy (may still be on the net), it is normally associated with piping configuration (elbows), also check the Re number in the main flow even if it is turbulent you can have a parabolic flow profile: high velocity in the center low velocity near the wall. This allows reduces the measured d/p for a given flow thru the orifice. I do not know what happens at your scale 5 & 2 mm

the inlet velocity correction is really for industial orifice plates, it was offered to illustrate that there are approach velocity issues involved.

you might be better off just measuring the d/p of a reduced diameter tube with the pressure taps in the inlet/outlet end pieces where the dimensions are larger.

 

[rcooper]

Are your downstream tappings far enough away from the orifice that the flow has fully expanded, rather than being a jet down the centre of the pipe. If it is far enough away, there will be some frictional losses. These could be measured by carrying out your tests without the orifice in place, and noting the pressure loss. The orifice is then placed in the pipe line and the additional loss arising from the orifice is measured.

 

[Feldmann359]

Hello!

Perhaps my downstream pressure tap is too far awy from the orifice bore! So in the simpified discharge coefficient formula cd=dm/dt / A0*sqrt(2*rho*dp), the dp is the pressure drop without pressure recovery? So if my pressure tap is there where the flow is again fully expanded, my pressure drop would be lower compared to the situation where the downstream pressure tap is located directly at the orifice bore.
So this would perhaps explain that my CD values are all higher than unity?

Greetings,
Stephan