dischargekoefficient

Discharge coefficient, abbreviated Cd, is a dimensionless factor used in fluid dynamics to quantify the loss of flow capacity when a fluid passes through a restriction such as an orifice, nozzle, or valve. It is defined as the ratio of the actual flow rate to the ideal flow rate under the same pressure drop. For incompressible, volumetric flow through a sharp-edged orifice, the relationship is often written as Q_actual = Cd × A × sqrt(2 × ΔP / ρ), where A is the cross-sectional area of the restriction, ΔP the pressure drop, and ρ the fluid density. The corresponding mass flow rate is m_dot = ρ × Q_actual.

Cd values are typically less than 1 and depend on geometry, flow regime, and fluid properties. Common devices exhibit different ranges: sharp-edged orifices often have Cd values around 0.6 to 0.65 under standard conditions, while venturi tubes and smooth nozzles can approach Cd values near 0.9 to 0.98. In practice, Cd is determined by calibration or from device-specific data provided by manufacturers or standard tables.

Several factors influence Cd, including the restriction’s geometry (such as beta ratio, the ratio of the restriction diameter to pipe diameter), edge sharpness, surface roughness, upstream and downstream pressure conditions, and the Reynolds number of the flow. For gases, compressibility and potential choking can alter the relationship, and an expansion factor or separate flow-regime treatment may be required.

Cd is a key parameter in flow metering and process control. It is used to convert measurable pressure drops into flow rates, often via calibration curves or standards (for example, ISO 5167) to ensure accurate, repeatable measurements.

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