Calculation of Beta Ratio - Intergraph Smart Instrumentation - Reference - Hexagon

1. Calculate internal pipe diameter at flow temperature:

   

2. Calculate correction factor for steam quality (for liquid, water, and steam, Fs=1):

   

3. Calculate scale reading factor:

   

4. Calculate differential pressure at normal flow rate:

   

5. Calculate pipe Reynolds number at normal flow rate:

   

6. Checking for critical flow.

   1. Liquid/Water case:

      1. If then the flow is critical.

   2. Gas/Steam case:

      1. For Venturi tubes:

         

      2. For other restriction devices:

         

      3. Calculate critical pressure ratio and define whether the flow is crtiical:

         

         If then the flow is critical. If not, the flow is sub-critical.

7. Calculate b - ratio.

   Case A Liquid/Water - critical flow

   1. Calculate DP.

      

   2. Calculate first estimate for b - ratio.

      For Venturi tubes:

      

      For other restriction devices:

      

   3. Eps=1.

   4. Calculate discharge coefficient. See the Appendix.

   5. Calculate the new b - ratio.

      

   6. Calculate the relative change in b - ratio.

   7. 

   8. Repeat steps d to f until the relative change in b - ratio is less than 0.0001.

Case B Gas/Steam - critical flow

1. Calculate gas expansion factor:

   

2. Calculate discharge coefficient. See the Appendix.

3. Calculate first estimate for b -ratio (Wn[1b/h], T[r], P1{psi-a}, D[in]:

   

4. Calculate orifice diameter at flow temperature:

   

5. Calculate bore Reynolds number at normal flow rate:

   

6. Calculate discharge coefficient. See the Appendix.

7. Calculate new b -ration in accordance with equations in step c.

Case C Sub Critical flow

1. First estimate for DPn:

   

2. Calculate first estimate for b - ratio.

   1. For Venturi tubes:

      

   2. For other restriction devices:

      

3. Calculate gas expansion factor (for liquids/water, Eps = 1)

   1. For Venturi tubes and nozzles:

      

   2. For orifice plates:

      

4. Calculate discharge coefficient. See the Appendix.

5. Calculate new b - ratio:

   

6. Calculate new DP.

   1. For classical Venturi tube:

      

   2. For Nozzles:

      

   3. For orifice plates:

      

7. Calculate new DPn:

   

8. Calculate the relative change in DPn:

   

9. In Case C, repeat steps c to h until the relative change in the DPn is less than 0.0001.

8. Calculate orifice diameter at flow temperature:

9. Calculate orifice diameter at ambient temperature.

1. For Venturi tubes and nozzles:

   

2. For orifice plates: