6 replies to this topic

[HKk]

Dear All ,

 

I am planning to fill a vessel with 30atm 147 C air available using a 1/2" pipe 500 m long . I wish to calculate the flow through the pipe .( with vessel at atmospheric condition initially) .

p1 = 30 atm

p2=1 atm

L=500 m

Sg=1

T=147+273=420k

d=15.8 mm

 

 

I have used Waymouth Equation to find the flow & has got a result of 125 NM3/Hr. Is it correct ? I am little doubtful as this does not take into account the exit , entracnce & valve etc. resistance coefficients.

 

I have tried to calculate the same using Darcy's equation for compressible fluids . If I calculate K

 

K=f*L/D

K=0.027*500/0.0158

K=854

 

If I add other resistance cofficients , It may become near to 860 ,But the problem here I encounter is that I cannot use Net Expansion factor & Limiting factors for sonic velocities curves as these are avaialble for K upto 100 only.

 

Please help .

 

Regards

[Art Montemayor]

What you are describing is UNSTEADY STATE fluid flow.  If that is correct, then you can't apply a STEADY STATE fluid flow equation - such as Darcy or the inferior Weymouth.

 

You describe a differentially increasing target pressure while flowing a compressible fluid.  This is a totally different set of circumstances than the tools you are trying to apply.

[fseipel]

Yes, initial flow rate is correct (close to what Darcy predicts; obviously depends on pipe roughness which you didn't state).  As Art indicates you need to integrate.  If you're just looking for an approximation, simply calculate the flow at say, p2=1 atm, p2=5atm, p2=10 atm, p2=15 atm, p2=20 atm, p=24 atm, p2=27 atm, p2=29 atm, p2=29.5 atm, p2=29.7 atm, p2=29.9 atm.  You should use tighter intervals as p2 approaches p1 since flow rate slows down.  Rules of Thumb for Chemical Engineers has a good spreadsheet for this -- you just goal seek to calculate flow given DP -- avoids unit errors and need for charts.  http://www.google.co...NF1wJYzsH2lkFEg

Once you have the instantaneous flow rate you can simply calculate how many lb-moles lie between two tank pressures (one interval) using ideal gas law and tank volume, divide by flow rate in same units, to calculate time to pressurize tank for that interval.  Summing the calculated times across all intervals will give total time to pressurize.

[HKk]

Dear Sir

 

Thanks  for your guidance .

 

Yes I have claculated the way it has been explained by you , using 1atm Dp as the interval . But I am worried about the fact that some conditions may fall into sonic velocity category . This sonic velocity conditions I am not able to find as K vs Dp/P chart is not available for K>100( I am refering Crane A-22 graph). Another way to check this is calculate velocity for each Dp interval ,Cross it with sonic velocity

& if sonic velocity is more then change to flow rate calculated with  the sonic velocity . But in the Darcy's equatiuon, there is a K & There is a Y factor ( net expansion factor ) which is K dependent . CAn I take Y as 0.710 as it is same for all 20<K=100 and K whatever is coming ( K~860 inthis case)

 

q=19.31Yd²*(√Dp*p/KTS_g)

 

Regards

[fseipel]

Yes, I understand; you cannot read the Y factor off because the Crane table stops at K=100 with the last several entries, converging upon Y=0.710.  Yes, use of 0.710 should be fine.  You also should be able to verify that by assessing a shorter segment of pipe, e.g. if K=860, assess a length of pipe 1/9 as long and thus DP/P' = 1/9 its value thus falling on table (i.e. below 100).  Now you are inside chart/table bounds.  This assumes your 'K' doesn't include the expansion at the outlet/tank since that should only be 'counted' once.  Since the flow must be the same everywhere in the pipe the calculated flow will be identical to the assessment of the overall length for a simple straight pipe.

Edited by fseipel, 02 October 2013 - 10:12 PM.

[latexman]

HKk,

 

Then use the isothermal flow equation (Equation 3-7 in my Crane) which has L, not K.  If you have fitting K's, convert them to Leq and add.

[HKk]

Thanks to eberybody for the help. I have found that it requires 32 1/2" pipes to replace 2 " pipe for same capacity in case of liquids & some 54 pipes for gases.

(d₁³*√d₂+3.6)/ (d₂³*√d₁+3.6) ( for gases)

(d₂/ d₁) ^2.5                                        (for liquids)

 

Ref :HandBook of Chemical Engineering Calculation by Nicholas P. Chopey

 

Is it correct to use these equations for calcution of relative carrying capacities.

 

Regards