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Basic Hydraulics of Flow Metering |
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Bernoulli Principle:
In a steady horizontal flow without friction, the sum of the velocity head and pressure head (P) (potential energy) is a constant quantity along any stream line.
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Equating the total head at the inlet and outlet throat sections: |
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The continuity equation for steady state flow states that the mass of fluid passing any flow section per unit of time is constant. Therefore: |
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{3} Q = AV1ρ1 = aV2ρ2 |
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Incompressible Flow: With an incompressible fluid, the density is constant and equation {3} becomes: |
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{4} AV1 = aV2 or {5} V1 =  (V2) |
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If the areas are circular, is usually replaced with |
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d2 = ß2 and equation {5} becomes: D2 {6} V1 = (ß2)(V2) |
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Using the value of V1 from equation {6}, substituting into equation {3}, and rearranging gives: |
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In general, differential pressure meter users are interested in knowing the flow rate in terms of the differential pressure produced. For the theoretical volume flow rate, Qt = (a)(V2), substituting for V2 from equation {7} and
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Equations {1} and {9} give "theoretical" rates (Qt) of flow which are never exactly equal to the "actual" rate (Qa) values. To obtain the actual flow rate, an additional factor, Coefficient of Discharge (CD) is used:
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The actual flow rate becomes: |
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Another factor has to be introduced to account for the change in the area "a" due to expansion/contraction when temperature changes are significant - more than ±50º F from the ambient temperature at which the meter was manufactured. When this Thermal Expansion Factor, Fa, is included, equation {12} becomes:
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For specific Fa values in applications where temperature changes are appreciable, contact your BIF representative. |
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Compressible Flow: The previous discussion dealt with incompressible liquids such as air or steam: |
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where Y is the adiabatic expansion factor and Ρ is at line conditions. For rough calculations, use y = 0.95. |
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The factor, Y, takes into account the difference in density of the fluid as its velocity changes through the throat of a differential pressure meter. The thermodynamic properties of the fluid determine the value of Y. To determine if a more precise result is needed, perform the following calculation: |
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If the term in parentheses is greater than 0.015 or an exact calculation is required, contact your BIF Representative. |
