3 replies to this topic

[garych]

Hi,

Do anyone come across the following equation when calculating the relieving flow rate for tube rupture case? 

 

F = 1.75 * ID^2 * ((OPH - DPL or PCF) * DN)^0.5  [kg/h]

      ID: Tube internal Diameter,

      OPH: Operating Pressur at high side,

      OPL; Operating Pressure at low side,

      PCF: Critical Pressure , DN: Density at high side

 

Do you have any idea how does the factor "1.75" come from?

[ahmadikh]

 Garych,

 

That is coming from the factors for dimensional balance (units of measurement balance) as well as applying a typical K factor, which is called the resistance factor. This resistance factor is due to the sudden expansion (flow from tube into shell) or reduction (flow from shell into tube) that the fluid flowing from high pressure side to the low pressure side faces in its path. Remember that you will have to double the number you get from this equation since the rupture may happen at the middle of the tube (This is true when you make sure that this equation is derived for one hole only!!). Also, you can consider 1.1*DPL to take some credit for the max allowable overpressure in the low pressure side.

 

Hope this helps...

 

Best,

Milad

[paulhorth]

Milad,

That answer does depend on what units are intended for the equation.

As written,in the original post, we have no idea whatsoever what units should be used for pressure, density, diameter.

 

Equations should never be quoted without defining the units of each term.

 

Paul

[garych]

Thanks for the reply.

I recently found out that in another post, there is a smiliar equation for calculating the tube rupture flowrate as stated below.

"Following the orifice theory, formulas to estimate flow rate can be of the form K*0.7*2*d^2*SQRT[(P1-P2)/sg], where K=dimensional constant, d=tube inside diameter, P1=normal operating pressure of high pressure side, P2=design pressure of low pressure side (there may be some variations of the formula). Factor 0.7 is the discharge coefficient; and factor 2 represents that flow occurs from both sides of ruptured tube (even though the one side is expected to get lower operating pressure after rupture)"

 

I am quite confused with how is the abovementioned equation is derived.

If we look at CRANE, the equation for calculating flow of gases and vapours (compressible flow) through an orifice, it is q= YCA(2*delta P/density)^0.5, in which Y is the expansibility factor and C is flow coefficient.

 

Can anyone please explained to me in details and what unit should i used for the equation?...