14 replies to this topic

[SPF]

I am trying to set up a Mathcad document in which we can carry out our Thermal Relief Valve sizing based on the API 520 method.

 

All was working fine until I tried to run equation number 29 - A=((11.788*Q)/(Kd*Kw*Kc*Kv))*sqrt(G1/(P1-P2))

 

Mathcad gives a result with the units m^(7/2) / kg^(1/2). The only reason I can think that this is (I've checked all the units and carried out a unit balance and got the same unit result as mathcad) is that the constant 11.788 is not actually dimensionless and to give me an area unit result, this constant must have a unit of kg^(1/2) / m^(1 1/2).

 

Can anyone confirm this? And if this is the case, what is the best way for me to get around Mathcad's automatic unit balancing to get the answer in cm^2 as the API suggests that the outcome of the equation should be?

 

Thanks in advance for any help.

 

Stuart

[PaoloPemi]

for Mathcad I recommend this resource

 

'http://www.harveyhen...roperties.html'

 

download the files and you will be able to size/rate

a PSV with HEM, HNE, NHNE methods  

[SPF]

Thanks for the advice Paolo but unfortunately the network I work off of will not allow download of Zip files of that sort.

[curious_cat]

 

Can anyone confirm this? And if this is the case, what is the best way for me to get around Mathcad's automatic unit balancing to get the answer in cm^2 as the API suggests that the outcome of the equation should be?

 

Why not explicitly include it as a dimensional constant?

[PaoloPemi]

when you solve for area = W / (K*sqrt(dens*dp))

you need to consider the units of flow, dp etc.

if these are predefined just convert to the unit required,

as suggested by curious_cat,

differently you need to redefine constants.

(by the way this is the reason why

I suggested to use that Mathcad

library which includes an automatic

unit conversion procedure)

Edited by PaoloPemi, 15 November 2013 - 04:54 AM.

[SPF]

Thanks curious_cat. I've tried adding replacing 11.78 with K and making K = 11.78 (kg^(1/2) / m^(1 1/2)) and this gives me a more sensible option which is in area units (a step in the right direction!) but it is still not the same value as you would get if you purely plugged values into the API calculation on your calculator.

[SPF]

I think basically I need to find where API 540 calculation 29 is derived from to find out the units of the constant but unfortunately I can't seem to find that.

[SPF]

As I work further through I am finding the same problem with equation 33 for calculating the Reynolds number with a dimensionless number causing havoc with the units.

I am thinking that maybe I should have stuck to a simpler Excel spreadsheet and surrender to writing up individual reports for each thermal relief valve.

[curious_cat]

 

I am thinking that maybe I should have stuck to a simpler Excel spreadsheet and surrender to writing up individual reports for each thermal relief valve.

 

No no. Don't give up yet. Yes, Excel may be easy but IMO what you are doing is indeed the right way. 

 

I think you'll figure it out and in the process figure a bit more about the origins of these equations. 

[SPF]

Thanks for the encouragement. I'll try and delve deeper into how the original equation was derived and maybe I'll find the key to unlock my condundrum there!

[curious_cat]

Thanks for the encouragement. I'll try and delve deeper into how the original equation was derived and maybe I'll find the key to unlock my condundrum there!

 

In this eq. can you define the various terms? 

 

A=((11.788*Q)/(Kd*Kw*Kc*Kv))*sqrt(G1/(P1-P2))

 

I assume A is area, P1, P2 are pressures. 

 

What are the other terms?

 

Assuming the three K's are dimensionless & that G is specific gravity, I get the same units for 11.788 as you do. i.e. kg^(1/2) / m^(1 1/2)

Edited by curious_cat, 15 November 2013 - 08:16 AM.

[curious_cat]

Your this statement I did not exactly understand:

 

 

 

 but it is still not the same value as you would get if you purely plugged values into the API calculation on your calculator.

 

Can you illustrate with actual numbers? I'll try replicating it. 

[breizh]

Hi,

Pay attention that A is expressed in mm2 ; Q (liters/minute) and Pressure (Kpa).

Hope this helps

 

Breizh

Edited by breizh, 18 November 2013 - 07:39 AM.

[SPF]

Curious_cat - the units are as follows:

 

 

Q is the required relief rate (L/min).

K_D is the coefficient of discharge. This can be obtained from the valve manufacturer but for preliminary sizing an effective discharge of 0.65 can be used when a PRV is installed with or without a rupture disk in combination, or 0.62 when a PRV is not installed and sizing is for a rupture disk.

K_W is the correction factor due to backpressure; if the backpressure is atmospheric, a value of 1.0 is used. Balanced bellows valves in backpressure service will require a correction factor that can be determined from Figure 31 in API 520. Conventional and pilot operated valves require no special correction.

K_C is the combination correction factor for installations with a rupture disk upstream of the PRV. The value of this is 1 when a rupture disk is not installed and 0.9 when a rupture disk is installed in combination witha PRV and the combination does not have a certified value.

K_Vis the correction factor due to viscosity

G is the specific gravity of the fluid (dimensionless)

P1 is the relieving pressure (kPag) – this is the set pressure (see below) plus 10% over-pressure.

P₂ is the total back-pressure (kPag)

Edited by SPF, 18 November 2013 - 03:46 AM.

[SPF]

 In my example,

 

Q = 5.141 l/min

Kd = 0.65

Kw = 1

Kc = 1

Kv =1

P2 = 82 kPa

P1 = 913 kPa

G = 0.73

 

Thanks again!