Orifice Flow Rate Calculator
Typically 0.6 – 0.65 for sharp edges
Water is approx. 1000 kg/m³
Calculated Flow Rate
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Understanding Flow Rate Through an Orifice
Calculating the flow rate through an orifice is a fundamental task in fluid mechanics and engineering. It describes the volume of fluid that passes through a constricted opening in a pipe or tank over a specific period.
The Orifice Flow Formula
The calculation is based on Bernoulli's principle. The standard equation used for volumetric flow rate (Q) is:
Q = Cd × A × √(2 × ΔP / ρ)
- Cd (Discharge Coefficient): This accounts for energy losses and the contraction of the fluid stream (vena contracta). For sharp-edged orifices, this is usually around 0.60 to 0.65.
- A (Orifice Area): The cross-sectional area of the opening. For a circular hole, A = π × (Diameter/2)².
- ΔP (Pressure Drop): The difference in pressure before and after the orifice.
- ρ (Density): The mass per unit volume of the fluid being measured.
Practical Example
Imagine you have a water tank with a 10mm hole (orifice) at the bottom. The water pressure at that depth is 50 kPa, and the density of water is 1000 kg/m³. If we assume a discharge coefficient of 0.62:
- Convert diameter to meters: 10mm = 0.01m.
- Calculate Area: π × (0.005)² = 0.0000785 m².
- Apply formula: 0.62 × 0.0000785 × √(2 × 50000 / 1000).
- Result: Approximately 0.000486 m³/s, which is roughly 29.2 Liters per minute.
Key Factors Influencing Accuracy
Several factors can affect the real-world flow rate compared to the theoretical calculation:
- Orifice Shape: Beveled or rounded edges have higher Cd values (closer to 0.98) than sharp edges.
- Viscosity: Highly viscous fluids (like honey) flow much slower and require different calculations.
- Reynolds Number: Flow characteristics change between laminar and turbulent states.