# Calculation of Beta Ratio - Intergraph Smart Instrumentation - 13.1 - Reference - Hexagon PPM

## Integraph Smart Instrumentation Sizing Equations

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Intergraph Smart Instrumentation
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Reference
Smart Instrumentation Version
13.1
1. Calculate internal pipe diameter at flow temperature:

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

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. 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: