RE: !!! RE: about surge

Thanks for Erik & Steve for ur explanation... now im understand.

Regards,

Firman Tuakia

On Mon, 24 Jan 2005, Steve McKenzie wrote:

>
> Gents
>
> for those of you who wish to do a search, the spelling is Joukowsky.
>
> Also for PVC celerity (wavespeed), 300m/s is a more typical value.
>
> Eric is buying a new keyboard as the 0 & o keys are a little sticky.
>
> Cheers
>
> Steve
>
> -----Original Message-----
> From: Erik Scheir [mailto:erik.scheir@pandora.be]
> Sent: Monday, January 24, 2005 9:37 PM
> To: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
> Subject: RE: !!! RE: [PipingDesign] about surge
>
>
>
> It is not so much the frequency but the magnitude who is of importance
> in waterhammer. There is a fundamental relation, called Jukowsky's
> equation, between pressure wave dH ,change of velocity of flow dV, and
> wave speed a.
>
> dH=dV*a/9.81
>
> Typical values for qa pipe containing water are:
>
> PVC a= 30 m/s, steel a= 1100 m/s
>
> Erik
>
>
>
>
> _____
>
> Van: Firman Tuakia [mailto:engineer@lmbsp.ms.itb.ac.id]
> Verzonden: zondag 23 januari 2005 14:44
> Aan: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
> Onderwerp: RE: !!! RE: [PipingDesign] about surge
>
>
>
>
> thanks for ur respons..
>
> 1.im talking abt instant closure of the valve.. i already figure it abt
> the 2L/a freq., but what i want to make it sure, is it true the
> frequency of oscillation only depend on L and a ..?
>
> Because what i understand: 2L/a = first mode of frequency of sound
> wave
> (the same as freq. for closed end pipe).
>
> If the 2L/a freq. is an accurate estimation, so if we have a quite
> long
> L,the frequency will be very high.
> Then I imagine abt the reflection, isn't the longer L the longer
> period
> of time needed --> the longer the period the shorter/smaller freq.
>
> 2. if i modelled the damping for the oscillation head only by friction
> (viscous damping equivalency) then it means i ignore the energy
> disspation at pounding/hammering that converted into heat & sound.
> is my model still accepted ?
>
>
> Thank you for you all..
>
>
> Regards,
>
> Firman Tuakia
>
>
>
>
>
>
> On Sun, 23 Jan 2005, Erik Scheir wrote:
>
>>
>> Are you talking about a pumptrip or closing a valve at the end of the
>> pipeline? The response time of a pressure wave is 2l/a where L =
>> pipelength and a= wavespeed.
>> The demping time is depending on the pipe roughness.
>> In case of a pumptrip if the rotational inertia of the centrifugal
> pump
> and
>> motor continue to rotate the pump for a while after power failure,
>> water hammer pressure transients may be reduced.
>>
>> Erik
>>
>>
>>
>>
>>
>> _____
>>
>> Van: Firman Tuakia [mailto:engineer@lmbsp.ms.itb.ac.id]
>> Verzonden: zaterdag 22 januari 2005 17:52
>> Aan: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>> Onderwerp: !!! RE: [PipingDesign] about surge
>>
>>
>>
>>
>> anybody please help me: how to plot the oscillating head/pressure
>> increase (when water hammer occur) at any point we want. especially
>> how to: 1. calculate the frequency of the oscillation
>> 2. estimating the damping tt causing the oscillated head/pressure
> become
>> stabil again (such as the respon of step function)
>>
>>
>> Thanks before..
>> Regards,
>>
>> Firman Tuakia
>>
>>
>>
>>
>> On Thu, 20 Jan 2005, Erik Scheir wrote:
>>
>>>
>>> Measurement of Pressure.
>>>
>>> Lets keep it simple:
>>>
>>> Perfect vacuum cannot exist on the surface of the earth, but it
>> nevertheless
>>> makes a convenient datum for the measurement of pressure.
>>>
>>> Barometric pressure is the levelof atmospheric pressure above perfect
>
>>> vacuum.
>>>
>>> "Standard" atmospheric pressure is 1.0325 bar (19.6959 lbf/in2) or
>>> 760 millimeters of mercury.
>>>
>>> Gauge pressure is measured above atmospheric pressure,while absolute
>>> pressure always refers to perfect cvacuum as a base.
>>>
>>> Vacuum is the depression of pressure below the atmospheric level.
>> Reference
>>> to vacuum conditions is often made byexpressing the absolute pressure
>
>>> in terms of the height of a column of mercury or of water.
>>>
>>> At least that's the way we define pressure in Europe.
>>> If it is still not clear, its always possible to graphically
>>> illustrate
>> the
>>> relationsship between gauge and absolute pressures.
>>>
>>> Erik
>>>
>>>
>>>
>>>
>>>
>>>
>>> _____
>>>
>>> Van: Steve McKenzie [mailto:mechproj@xtra.co.nz]
>>> Verzonden: woensdag 19 januari 2005 23:06
>>> Aan: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>> Onderwerp: RE: [PipingDesign] about surge
>>>
>>>
>>> Hi Al
>>>
>>> much as I enjoy deception, it was not used intentionally in this
>>> case. My Patm is 2bara being the sum of sealevel air pressure of
>>> 1bara plus the submergence of 10.2m or 1 bar. As you go deeper the
>>> pressure in the bell gets higher. It is my Pgauge that is -2. This
>>> condition could conveivably occur in a subsea line under water hammer
>
>>> conditions. Eriks contention is that you cannot go less that -1 barg
>>> while I maintain it depends what value you put on Patm. A bourdon
>>> tube pressure gauge measures the pressure differential between the
>>> inside and outside of the tube. With 2 bara on the outside and 0bara
>>> on the inside it would try to read -2, scale and mechanicals
>>> permitting. If you enclose an unconnected pressure gauge in a vacuum
>>> chamber, the needle should rise to about 1 bar, as there is no
>>> external pressure pushing the needle back to 0bar (must try this).
>>>
>>> The grey area it whether or not the pressure in the bell can be
>>> called Patm. Its easy to do in practical terms; just use a DP gauge
>>> with the HP leg disconnected and the LP leg to the pipe.
>>>
>>> I hope you remember to remove the vent plug when you install a
>>> pressure gauge, otherwise your Patm becomes the pressure inside the
>>> gauge casing instead of the surroundings. In hot places, with a well
>>> sealed case the difference could be considerable.
>>>
>>> Cheers
>>>
>>> Steve
>>>
>>>
>>> -----Original Message-----
>>> From: aluser2 [mailto:alwynk@shaw.ca]
>>> Sent: Thursday, January 20, 2005 8:15 AM
>>> To: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>> Cc: aluser2; <a href="/group/PipingDesign/post?postID=BO6c0_69FruURepsOTLDCFKuov2C6U9Mq89V4UQ41b0TnDxJ0onGQjfq_bCm7VFjKNjN80IvFFt4">mechproj@xtra.co.nz</a>
>>> Subject: Re: [PipingDesign] about surge
>>>
>>>
>>>
>>> tsk tsk.
>>>
>>> math sleight of hand steve. U switched from local atmos pressure in
>>> absolute to saying it was the gauge reading (barg)
>>>
>>> "Gauge pressure is defined as Pabs - Patm = 0bara - 2bar(a)
>>> not= -2barg. not QED"
>>> ie your Patm is not -2barg.
>>>
>>> your gauge pressure is PAbs- Patm = 0bara- 2bara (as defined in your
>
>>> first
>>> line>ie. not 0barg-2barg)
>>> so the gauge pressure on the tube would be -2bara = -1barg (i'm in NA
>
>>> and years since i used bar , but i recall1 bar absolute is
>>> 101kpa=14.7psia. and 1bar gauge is 14.7psig (relative to atmos ie on
>>> top of earths 14.7pisa so (-2bara not -2barg). ie you wouldnt read
>>> this on a gauge.
>>>
>>> so the gauge would read -1bar (ie complete vacuum) (relative to the
>>> ambient bell pressure) which is possible as you say with a vacuum
>>> gauge. the riddle missed the sealed ends of the pipe which we assumed
>
>>> was what you meant.
>>>
>>> Practical problem - since a normal gauge measures relative to the
>>> surroundings you would have to be sure the gauge was able/calibrated
>>> to handle the bell submersed (environmental ambient pressure -32feet
>>> ). do i sense a troll? .
>>> ----- Original Message -----
>>> From: "Steve McKenzie" <mechproj@xtra.co.nz>
>>> To: <PipingDesign@yahoogroups.com>
>>> Sent: Tuesday, January 18, 2005 7:32 PM
>>> Subject: RE: [PipingDesign] about surge
>>>
>>>
>>>>
>>>> Hi Erik
>>>>
>>>> Local air atmospheric pressure inside air bell is P atm = 1 barg + 1
>
>>>> bara = 2 bara . Pressure inside pipe is P abs = 0 bara.
>>>>
>>>> Gauge pressure is defined as Pabs - Patm = 0 - 2 = -2barg. QED.
>>>> However you will probably have to use a DP gauge to measure.
>>>>
>>>> I think most engineers can design a pipe (or a bell) which will
>>>> stand a vacuum by designing to stay below the critical buckling
>>>> pressure.
>>>>
>>>> Either run the pipe through the sides of the air bell (sealed at the
>>>> intersections) or run the pipe up into and down out of the air
>>>> bell, or have the pipe sealed at both ends.
>>>>
>>>> We engineers can do anything!
>>>>
>>>> Cheers
>>>>
>>>> Steve
>>>>
>>>>
>>>>
>>>> -----Original Message-----
>>>> From: Erik Scheir [mailto:erik.scheir@pandora.be]
>>>> Sent: Tuesday, January 18, 2005 8:12 AM
>>>> To: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>>> Subject: RE: [PipingDesign] about surge
>>>>
>>>>
>>>>
>>>> If the pressure above the waterlevel is atmospheric, then the
>>>> pressure
>>>
>>>> 10.3 m below the waterlevel is 1 barg (gauge) and an air bel with a
>>>> 100% vacuum will collapse.
>>>>
>>>> How can you run a pipe through an air bell?
>>>>
>>>> Cheers,
>>>>
>>>> Erik
>>>>
>>>>
>>>>
>>>> _____
>>>>
>>>> Van: Steve McKenzie [mailto:mechproj@xtra.co.nz]
>>>> Verzonden: zondag 16 januari 2005 19:46
>>>> Aan: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>>> Onderwerp: RE: [PipingDesign] about surge
>>>>
>>>>
>>>> I am normally not one to split hairs, but couldn't resist this one:
>>>> Consider an air bell 10.3m below water level, with a (perfect)
>>>> vacuum
>>>
>>>> pipe passing through it. Inside the air bell is a pressure gauge
>>>> connected to the pipe. What is the gauge pressure?
>>>>
>>>> Cheers
>>>>
>>>> Steve
>>>> -----Original Message-----
>>>> From: Erik Scheir [mailto:erik.scheir@pandora.be]
>>>> Sent: Sunday, January 16, 2005 11:45 PM
>>>> To: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>>> Subject: RE: [PipingDesign] about surge
>>>>
>>>>
>>>>
>>>> I used this sofware perhaps even before you were born, but what has
>>>> that to do with te fact that -2 bar does nor exist on the earth. Try
>
>>>> to use Flowmaster its even better then impulse from AFT and you will
>
>>>> never see results with pressure nodes below 0 bar.
>>>>
>>>> Erik
>>>>
>>>>
>>>>
>>>>
>>>> _____
>>>>
>>>> Van: gautam wayse [mailto:captain_wayse@yahoo.co.in]
>>>> Verzonden: zaterdag 15 januari 2005 9:30
>>>> Aan: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>>> Onderwerp: RE: [PipingDesign] about surge
>>>>
>>>>
>>>>
>>>> hi
>>>> friend
>>>> better to go for impulse software for surge analysis
>>>> .from applied flow technology,.
>>>> use --- Erik Scheir <erik.scheir@pandora.be> wrote:
>>>>
>>>> ---------------------------------
>>>> What do you mean with - 2 bar? Is it barg?
>>>> The absolute vacum is - 1 barg or 0 bara, so - 2bar
>>>> doesn't exsist.
>>>>
>>>> erik
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> -----Oorspronkelijk bericht-----
>>>> Van: Omid Hamlehdar [mailto:omid_7_ae@yahoo.com]
>>>> Verzonden: dinsdag 11 januari 2005 7:19
>>>> Aan: <a href="/group/PipingDesign/post?postID=2-dMMVkCFPC16CXaL-XyngulI_lfdFVat4E9mffgZvLCmnrNRYP0Zz3erRl_136kYlk2Aovz0--YChANnUKC2F_BONk">PipingDesign@yahoogroups.com</a>
>>>> CC: mechproj@xtra.co.nz; <a href="/group/PipingDesign/post?postID=MWIRuj3Z03WiSCJzEYNTbeFKhn75YdnL2eq0ZdKc7JhrhG7bmkTl49zMCFSPcLya8wB3rwwXRMjsI5oSyfDpcjo">erik.scheir@pandora.be</a>
>>>> Onderwerp: [PipingDesign] about surge
>>>>
>>>>
>>>>
>>>> Hi all
>>>>
>>>>
>>>>
>>>> I have a project for water handling, a pipeline with
>>>> 100 km length, I am
>>>> studying about surge in it according to a probable
>>>> rapture in pipe and I am
>>>> going to close two valves surrounding rapture point to avoid wasting
>
>>>> water and to find out about surge cause by closing valves.
>>>>
>>>> Any body has experience in this regards? How shall we protect our
>>>> system?
>>>>
>>>> I have heard from Erhard valve, they recommend a valve called "pipe
>>>> burst control valve" to avoid wasting water when there is a rapture,
>
>>>> this valve will be closed in around 2 min and this will cause
>>>> surge in system, in some
>>>> point we have -2 bar minimum pressure. I know that you
>>>> may need to know
>>>> about the profile but generally I would like to know
>>>> how shall we suppress
>>>> this surge?
>>>>
>>>>
>>>>
>>>> Best regards
>>>>
>>>>
>>>>
>>>> Omid
>>>>
>>>>
>>>>
>>>> ---------------------------------
>>>> Do you Yahoo!?
>>>> The all-new My Yahoo! - What will yours do?
>>>>
>>>> [Non-text portions of this message have been removed]
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping
>>>> Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping
>>>> Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>>
>>>>
>>>>
>>>> ---------------------------------
>>>> Yahoo! Groups Links
>>>>
>>>> To visit your group on the web, go to:
>>>> <a href="http://groups.yahoo.com/group/PipingDesign/">http://groups.yahoo.com/group/PipingDesign/</a>
>>>>
>>>> To unsubscribe from this group, send an email to:
>>>> <a href="/group/PipingDesign/post?postID=0KCACnB4FJ36B7ssSIzHR2YIrrVaquwQGMpQHmL1-AeBOhQSDwIqYdHth9qH8OmTgqJw_Is_RH3hoiiAoNMch7o2BxqCoiCMb6YcWUZeOQ">PipingDesign-unsubscribe@yahoogroups.com</a>
>>>>
>>>> Your use of Yahoo! Groups is subject to the Yahoo!
>>>> Terms of Service.
>>>>
>>>>
>>>> ____________________________________________________________________
>>>> __
>>>> __
>>>> Yahoo! India Matrimony: Find your life partner online
>>>> Go to: <a href="http://yahoo.shaadi.com/india-matrimony">http://yahoo.shaadi.com/india-matrimony</a>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>>
>>>>
>>>>
>>>> _____
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>>
>>>> * To visit your group on the web, go to:
>>>> <a href="http://groups.yahoo.com/group/PipingDesign/">http://groups.yahoo.com/group/PipingDesign/</a>
>>>>
>>>>
>>>> * To unsubscribe from this group, send an email to:
>>>> <a href="/group/PipingDesign/post?postID=0KCACnB4FJ36B7ssSIzHR2YIrrVaquwQGMpQHmL1-AeBOhQSDwIqYdHth9qH8OmTgqJw_Is_RH3hoiiAoNMch7o2BxqCoiCMb6YcWUZeOQ">PipingDesign-unsubscribe@yahoogroups.com</a>
>>>> <mailto:PipingDesign-unsubscribe@yahoogroups.com?subject=Unsubscribe
>>>>>
>>>>
>>>>
>>>> * Your use of Yahoo! Groups is subject to the Yahoo! Terms of
>>>> Service
>>>> <http://docs.yahoo.com/info/terms/> .
>>>>
>>>>
>>>>
>>>>
>>>> [Non-text portions of this message have been removed]
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>>
>>>>
>>>>
>>>> _____
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>>
>>>> * To visit your group on the web, go to:
>>>> <a href="http://groups.yahoo.com/group/PipingDesign/">http://groups.yahoo.com/group/PipingDesign/</a>
>>>>
>>>>
>>>> * To unsubscribe from this group, send an email to:
>>>> <a href="/group/PipingDesign/post?postID=0KCACnB4FJ36B7ssSIzHR2YIrrVaquwQGMpQHmL1-AeBOhQSDwIqYdHth9qH8OmTgqJw_Is_RH3hoiiAoNMch7o2BxqCoiCMb6YcWUZeOQ">PipingDesign-unsubscribe@yahoogroups.com</a>
>>>> <mailto:PipingDesign-unsubscribe@yahoogroups.com?subject=Unsubscribe
>>>>>
>>>>
>>>>
>>>> * Your use of Yahoo! Groups is subject to the Yahoo! Terms of
>>>> Service <http://docs.yahoo.com/info/terms/> .
>>>>
>>>>
>>>>
>>>>
>>>> [Non-text portions of this message have been removed]
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> =========================================
>>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>>> <a href="http://www.pipingoffice.us/">http://www.pipingoffice.us/</a>
>>>> =========================================
>>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>>
>>> =========================================
>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>> http://www.pipingoffice.us/ =========================================
>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>
>>> Yahoo! Groups Links
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> =========================================
>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>> http://www.pipingoffice.us/ =========================================
>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>
>>>
>>>
>>>
>>> _____
>>>
>>> Yahoo! Groups Links
>>>
>>>
>>> * To visit your group on the web, go to:
>>> <a href="http://groups.yahoo.com/group/PipingDesign/">http://groups.yahoo.com/group/PipingDesign/</a>
>>>
>>>
>>> * To unsubscribe from this group, send an email to:
>>> <a href="/group/PipingDesign/post?postID=0KCACnB4FJ36B7ssSIzHR2YIrrVaquwQGMpQHmL1-AeBOhQSDwIqYdHth9qH8OmTgqJw_Is_RH3hoiiAoNMch7o2BxqCoiCMb6YcWUZeOQ">PipingDesign-unsubscribe@yahoogroups.com</a>
>>> <mailto:PipingDesign-unsubscribe@yahoogroups.com?subject=Unsubscribe>
>>>
>>>
>>> * Your use of Yahoo! Groups is subject to the Yahoo! Terms of
> Service
>>> <http://docs.yahoo.com/info/terms/> .
>>>
>>>
>>>
>>>
>>> [Non-text portions of this message have been removed]
>>>
>>>
>>>
>>>
>>> =========================================
>>> PipingOffice - Excel Spreadsheets for Piping Calculations
>>> http://www.pipingoffice.us/ =========================================
>>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>>
>>> Yahoo! Groups Links
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>>
>>
>>
>>
>> =========================================
>> PipingOffice - Excel Spreadsheets for Piping Calculations
>> http://www.pipingoffice.us/ =========================================
>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>
>>
>>
>>
>> _____
>>
>> Yahoo! Groups Links
>>
>>
>> * To visit your group on the web, go to:
>> <a href="http://groups.yahoo.com/group/PipingDesign/">http://groups.yahoo.com/group/PipingDesign/</a>
>>
>>
>> * To unsubscribe from this group, send an email to:
>> <a href="/group/PipingDesign/post?postID=0KCACnB4FJ36B7ssSIzHR2YIrrVaquwQGMpQHmL1-AeBOhQSDwIqYdHth9qH8OmTgqJw_Is_RH3hoiiAoNMch7o2BxqCoiCMb6YcWUZeOQ">PipingDesign-unsubscribe@yahoogroups.com</a>
>> <mailto:PipingDesign-unsubscribe@yahoogroups.com?subject=Unsubscribe>
>>
>>
>> * Your use of Yahoo! Groups is subject to the Yahoo! Terms of
> Service
>> <http://docs.yahoo.com/info/terms/> .
>>
>>
>>
>>
>> [Non-text portions of this message have been removed]
>>
>>
>>
>>
>> =========================================
>> PipingOffice - Excel Spreadsheets for Piping Calculations
>> http://www.pipingoffice.us/ =========================================
>> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>>
>> Yahoo! Groups Links
>>
>>
>>
>>
>>
>>
>>
>
>
>
>
>
> =========================================
> PipingOffice - Excel Spreadsheets for Piping Calculations
> http://www.pipingoffice.us/ =========================================
> Main site: <a href="http://www.pipingdesign.com">http://www.pipingdesign.com</a>
>
>
>
>
> _____
>
> Yahoo! Groups Links
>
>
> * To visit your group on the web, go to:
> <a href="http://groups.yahoo.com/group/PipingDesign/">http://groups.yahoo.com/group/PipingDesign/</a>
>
>
> * To unsubscribe from this group, send an email to:
> <a href="/group/PipingDesign/post?postID=0KCACnB4FJ36B7ssSIzHR2YIrrVaquwQGMpQHmL1-AeBOhQSDwIqYdHth9qH8OmTgqJw_Is_RH3hoiiAoNMch7o2BxqCoiCMb6YcWUZeOQ">Piping"
Received on Mon Jan 24 07:25:00 2005