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

## Integraph Smart Instrumentation Sizing Equations

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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. 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: 