Sizing orifice (LIQUID)

[ddkm]

Sorry to those who may feel a sense of dejavu. But I do have some questions regarding sizing of orifices for LIQUIDS. Of course, we already have a good solid discussion on the similar topic here Thread: Flow of VAPOR thru a hole , but I didn't want to clog up the thread, so I've created a new one here.


Goes like this.

From Crowl/Louvar

Flow of Liq Through A Hole

The mass flow rate Qm due to a hole of area A is given by

Qm = A Co SQRT (2 rho gc DeltaP)
= A Co SQRT (2 rho gc Pg)


The literature assumes pressure in the external surroundings is atmospheric, therefore DeltaP = Pg

where:

A = leak cross sectional area (in ft2)
Co = discharge coefficient*
rho = liquid density
gc = gravitational constant (32.17ft lbm/lbf s2)
Pg = constant gauge Pressure within the process unit
P = constant gauge Pressure in external surroundings

But for my application, there is an external pressure, so I've remodified the equation as follows:
Qm = A Co SQRT (2 rho gc (Pg - P))



Problem:
Hot water being used as a cooling medium in a coil. The outlet of this (after the cooling) is steam, which is flashed off into a flash vessel. In this case, I assume that the pressure in "external surrounding" (i.e. P) cannot be atmospheric, but would be the pressure of the flashed steam.
The objective of the calculation is to size an orifice to limit the flow to 1700kg/hr. Using the above equation, we should vary the orifice diameter (and thus A) to get Qm that is required.

Questions:
1) Are the above the right basic equations to be used for sizing of orifice?
2) Complication of liquid in the incoming stream, but converted to vapour in the outlet (after the orifice and coil)
3) There is one pump for the hot water supply but branches into two coils. The orifice will be placed in each coil. Do we use the above equation separately for each coil?

Thanks in advance.

---engineering your life---

 

[katmar]

Does your system guarantee that there is no flashing across the orifice? If the downstream side of the orifice is below the saturation pressure of the water then it will flash as it exits the orifice and this behavior is very different from the equation you have presented.

 

[ddkm]

katmar:

you're up early What time is it over at South Africa?

Back to the question. I was wondering the same thing, but my current assumption is that it remains liquid (hot water) immediately after the orifice because the orifice will be located outside (prior to) the medium being cooled. The medium being cooled is actually liquid contents inside a reactor at temperatures up to 250C.

My guess is that the hot water will only flash inside the reactor environment. And as such, we could probably still apply the equation for a "liquid" phase assumption.


---engineering your life---

 

[katmar]

South Africa is 2 hours ahead of Britain at this time of year, so I wasn't up that early!

If the orifice is on the inlet to the coil then you are correct and the water calculation will be applicable. If the water is vapourising in the coil it will affect your heat transfer and your pressure drop calculations. In similar situations I have put an orifice or a valve at the outlet to ensure that the water does not vapourise in the coil, but it all depends on your requirements.

 

[mbeychok]

ddkm:

The Crowl and Lothar equation you quoted accounts only for the difference between the upstream source pressure and the the downstream pressure. If the source also has a liquid head, then you need to add that liquid head to the source pressure to obtain the instantaneous initial flow rate.

If the diameter of your coil is fairly small, then the liquid head is most probably insignificant. However, I wanted you to be aware that the equation you are using needed modification if there is a liquid head in the source.

Katmar is correct, if the liquid is saturated (i.e., at its boiling point for the source pressure), then the equation you are using is incorrect. I suggest that you visit www.air-dispersion.com/source.html, select whether you want SI metric or USA units, and then read "Liquid Discharge From a Pressurized Source". Then you should also read "Discharge of Flashing Saturated Liquid".

Milt Beychok

 

[mbeychok]

Oops!! My first sentence should read "The Crowl and Louvar equation ..."

Milt Beychok

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

 

[katmar]

Milton,

I realize that your equations are primarily aimed at accidental releases to atmosphere, but over the years I have looked at various ways of modeling the use of an orifice as a steam trap, and I wondered if you have ever tried this?

Before ddkm explained that the orifice was at the inlet to the coil, I assumed that he was putting it at the outlet and that would make it function much like a steam trap. I have done a bit of work in sugar mills where they use very low pressure steam (<15 psig) and with the huge difference in density between condensate and steam at these pressures I have tried to persuade clients to use orifices in place of the enormous and expensive low pressure traps. So far I have been totally unsuccessful in persuading anybody to try it, and I would be interested to know if you have used these equations for that purpose.

regards
Harvey

 

[mbeychok]

Harvey:

As you said, my major interest in the equations presented in

http://www.air-dispersion/source.html

is to determine the flow rate of accidental releases of gases or liquids to the atmosphere under various different conditions. Sorry, but I have no knowledge of anyone having tried to use orifices as steam traps.

Milt Beychok

 

[ddkm]

Milton:

"...equation you quoted accounts only for the difference between the upstream source pressure and the the downstream pressure. If the source also has a liquid head, then you need to add that liquid head to the source pressure to obtain the instantaneous initial flow rate."

Could you elaborate a bit more on this? Isn't the upstream source pressure the liquid head itself? This is assuming that the liquid (hot water) is being pumped from a tank and heated (thru heat exchanger) on the way into the coil.


---engineering your life---

 

[ddkm]

Having said the above, I need to clarify further. Didn't want to put it in earlier, as it was complicated enough.

Prior to entering the coil/orifice, the pumped liquid (hot water) actually goes through an expansion - the piping goes from a 40mm diameter and into a 150mm diameter. I haven't had time to think this through (as I'm in a bit of a rush, sorry), but will this expansion create some flash already? The hotwater goes in at about 110-120ºC which of course is already boiling at atmospheric conditions.

I've yet to verify the incoming pressure. Sorry for the sketchy details.

---engineering your life---

 

[mbeychok]

ddkm:

I did say if the source also has a liquid head ...". For example, if you had a closed tank or vessel that was say half full of hot water or any other liquid ... and you had a pressure gauge on the top of the tank or vessel. That gauge would only measure the pressure in the vapor space. But the total pressure at the bottom of the tank would be the pressure in the vapor space plus the liquid head of the liquid in the tank or vessel.

Once again, I urge you to visit www.air-dispersion.com/source, select whether you want USA units or SI metric units and then read the section on "Discharge From Pressurized Vessel". I know the author and he can be trusted.

Milt Beychok

 

[sailoday28]

Flow thru an orifice may go thru a minimum area (vena-contracta). Something of a venturi effect. At the vena contracta, the higher velocity results in a minimum presssure within the orifice. Downstream of the vena-contracta, within the orifice, the velocity decreases,with a further increase in pressure. Upon reaching the exit, the pressure is basically the downstream pressure.

If the downstream pressure is decreased, yet above the minimum pressure within the orifice, flow increases. Cavitaion, or vaporization at the vena-contraca is possible with the downstream pressure greater than the saturation pressure of the liquid.
Basically, what is apparantely a cold liquid, may flash thru an orifice, with what seems to be non-flashing back pressures.

 

[ddkm]

Milton:

[gray]"the total pressure at the bottom of the tank would be the pressure in the vapor space plus the liquid head of the liquid in the tank or vessel."[/gray]

Ok, liquid head would be significant if the tank was very tall. But I would normally exclude the pressure in the vapor space, as I would (rightly or wrongly) assume that this would be quite insignificant to the impact on the calculation?

By the way, I had already printed out the contents of your website during the discussion on the flow of vapour thru orifice. Very useful writeup you have, but I'm still taking some time to read it.

---engineering your life---