Estimating Expansion Factor in Fluid Flow Measurement
What is the expansion factor in a given scenario where air flows through a 10-cm-i.d. pipe with a square-edged orifice meter of 5 cm in diameter, if the upstream pressure in the pipe is 100 kPa and the pressure differential is 10 kPa?
Estimating the Expansion Factor:
To estimate the expansion factor in the given scenario, we can use the concept of the pressure differential and the properties of the orifice meter.
The expansion factor (β) is defined as the ratio of the actual flow area to the theoretical flow area. It accounts for the contraction of the flow as it passes through the orifice.
In this case, the orifice hole has a diameter of 5 cm, which corresponds to a radius (r) of 2.5 cm or 0.025 m.
The theoretical flow area (A(theoretical)) can be calculated using the formula for the area of a circle:
A(theoretical) = π * (r²) = π * (0.025 m)² = 0.00196 m²
The actual flow area (A(actual)) is related to the inner diameter (ID) of the pipe. The ID is given as 10 cm, which corresponds to a radius of 5 cm or 0.05 m.
A(actual) = π * (r(actual)²) = π * (0.05 m)² = 0.0079 m²
Now, we can calculate the expansion factor:
β = A(actual) / A(theoretical) = 0.0079 m² / 0.00196 m² = 4.03
Therefore, the estimated expansion factor in this scenario is approximately 4.03.