Steam Flow calcs thru Orifice - what formula to use 2

[carbluff]

thread391-246002
Just joined because I too am trying to double check flow calc of steam thru an orifice. Mr Rosse gave the flow in lb/hr answers for various drops but I've been struggling with all the forumulas to come up with proper units.
Mr Rosse, what formula (or calculator) did you use to get the flow answers?

 

[hectorjps]

hi i think you can use Q=AV that is the same Q=mv
Q is flow
m mass flow (lb/hr)
v specific volume
you need to know the properties of the steam it depends on the pressure temperatura etc.
hope this helps you

 

[casflo]

It is the typical equation to calculate the flow through an orifice. Flow(pounds/h) = 1891(d**2)YC(PD/v)**0.5
d ... orifice diameter, in
Y ... expansion factor for steam
C ... flow coefficient for squared edge orifices
v ... specific volume of steam (ft**3/pound)
You must see for example the Crane Technical Paper 410.
NOTE: The steam flow through squared edge orifices increase with pressure drop without limits by critical conditions.

casflo

 

[steamdog]

Careful with any equation for steam flow, they presume 100% dry quality steam. Any condensate in the steam will flash through the orifice choking the flow (like if you are trying to calculate the steam loss through a steam trap)

 

[carbluff]

still not getting the calc to match what the vendor sent me (from his program).

Here's what he sent:
in a 2.5" sch 40 pipe with a 1.664 bore orifice 200 inches H2O max drop gives 6,000 lb/hr of 160# (gage) steam entering.

The units don't seem right for the PD
The typical orifice drop is inches of H20 but that can't be right so converting to lb/inch2 still looks goofy.
I have the Crane manual but units not spelled out too well in that either.

What I'm trying to do is plug in a different pressure drop (actual read in the field during operating conditions) and get what the "new" flow would be. I'm no where close in getting the original flow, so need help.

 

[casflo]

For dry and saturated steam at inlet pressure of 160 psi the specific volume is 2.6 cubic ft/pound and C = 0.675,
Y = 0.62 for the suqared edge 1.664 orifice the flow is 17190 ponds/h if pressure drop = 160 psi.

 

[ione]

Carbluff,

This is the way they’ve probably got their result:

http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm

density for steam at 160 psig = 6.146 kg/m3

I have anyway some doubts it is correct.


Casflo,

How have you computed the expansion factor Y, as it is a function of both geometry (D1/D2) and Reynolds number (Re), and Re depends on velocity and so on flow (which is unknown)?

 

[katmar]

carbluff, the missing critical piece of information is where you are measuring the pressure differential.

Orifices are used for 2 entirely different purposes. The one is as a flow element to be able to measure the flow rate, and the second is to add resistance into the system to restrict the flow. It seems from your numbers that your orifice fits into the first category - i.e. you are trying to measure the flow rate. In this case the pressure differential is measured very close to the orifice plate. Examples of this are corner taps, flange taps or D and D/2 taps.

However, when you are trying to restrict the flow you are interested in the pressure differential relatively far away from the plate - maybe 2 diameters upstream and 10 diameters downstream. This is called the overall pressure drop. The examples in Crane are for this type of orifice. Crane addresses the overall pressure drop of a system so that it can be matched to a pump or other pressure source. The Crane manual makes no pretense of being an instrumentation manual and does not address the use of an orifice for measurement purposes.

The pressure drop measured across the close tapping points is always higher than the widely spaced points because you get pressure recovery downstream of the orifice. You must be aware which of these two pressure differentials your formula is trying to calculate.

The value of 200 inch of water seems reasonable to me for close taps - i.e. those designed for measuring a flow rate. I do not have my software with me at the moment so I cannot say it is exactly right, but it seems OK. Certainly not way out.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[casflo]

ione, I have computed C for turbulent flow, so it´s independent of Re number and Y depends on D1/D2 and DP/P.

 

[FredRosse]

The formula used is the general compressible flow equation, available in many Fluid Flow Books.

Mdot = Cd A { (2x/(x-1)) P1 Roh1 (P2/P1)^(2/x) [ 1 - (P2/P1)^((x-1)/x)] }^0.5

Where Cd = Orifice discharge coefficient (dimensionless)
A = Flow Area of Orifice (Length^2)
x = Specific Heat Ratio, Cp/Cv (dimensionless)
P1 = Inlet Pressure (Force per Unit Area)
P2 = Outlet Pressure (Force per Unit Area)
Roh1 = Inlet Density (Mass per unit Volume)

This equation is good for limit of (P2/P1) greater than:
(2/(x+1)^[x/(x-1)]

For P2 less than the above limit, then there is choked flow, and lower P2 will not give an increased flowrate, use (P1/P2) in the equation equal to (2/(x+1)^[x/(x-1)]

This equation is generic, is dimensionally consistent, and works in any rational system of units. Check the units within the equation. A common error is to use bastard units, which will show up immediately if the answer does not come up as mass flow per unit of time.

 

[casflo]

The compressible flow through squared edge orifices doesn´t have choked conditions. When P2 decreases the flow increases. See for example in the Crane Technical Paper 410 that the Y expansion factor has no limits as for nozzles or venturi meters.

casflo

 

[PaoloPemi]

With thin square-edged plates I presume the overpressure peak due to the speed of sound limit doesn't originate, Cunningham gives C=0.608+0.415*(d/D)^4 verified up to Pin/Pout about 5

 

[FredRosse]

The general equation is for one dimensional single restriction flow, applicable to nozzles and venturis and flow geometries which assure essentially these conditions. This approximation is ok for many applications, however the expansion factor equations are more accurate for conditions which differ significantly from one dimensional single restriction flow.

casflo is correct, "When P2 decreases the flow increases", however there is choked flow for low values of P2.

The actual conditions for a sharp edged or square edged orifice allow the choking surface to change in shape, giving a larger net choking area as the pressure differential increases. This in turn allows flow to increase with further decrease in downstream pressure, even with the limit of sonic velocity across the choked surface.

 

[carbluff]

This is fun. I've spent some time with ear plugs in at my desk trying to get the number.
Katmar, you are correct in that the field readings are coming from a tapped flange so maybe the formulas are moot.

Just for sanity check, I'm having a hard time figuring out in the formula that's widely used, how you can divide PD (in lb/in^2) by v (in in^3/lb). Don't you get lb^2 over in^5??? How do you take square root of a 5th and expect the units to come out.
I'm obviously missing something.

 

[FredRosse]

To be dimensionally correct, we need to always differentiate between Pounds(force) and Pounds(mass). They are not the same, and if you do not label them differently, there will be errors. I always use Lbf and Lbm. In our English Engineering system, they are related as follows:

F = M * A

1 Lbf = 1 Lbm * 32.2 ft / sec^2

This is easy to remember, if an object having a mass of one Pound(mass), under the influence of standard gravitational acceleration ( 32.2 ft / sec^2 ), it will exert a force of one Pound(force)on the table that is supporting it.

Many bastard formulas have various conversions built into them, and you cannot apply dimensional analysis. The fundamental equations are dimensionally consistent, and will always check out properly when units are applied and evaluated.