Power Number
Power number formula |
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\( N_p \;=\; \dfrac{P }{ \rho \cdot n^3 \cdot d^5} \) (Power Number) \( P \;=\; N_p \cdot \rho \cdot n^3 \cdot d^5 \) \( \rho \;=\; \dfrac{P }{ N_p \cdot n^3 \cdot d^5} \) \( n \;=\; \left( \dfrac{P }{ N_p \cdot \rho \cdot d^5} \right)^{1/3} \) \( d \;=\; \left( \dfrac{P }{ N_p \cdot \rho \cdot n^3} \right)^{1/5} \) |
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Symbol | English | Metric |
\( N_p \) = Power Number | \(dimensionless\) | \(dimensionless\) |
\( P \) = Power Input to the Fluid | \(ft-lbf \;/\; sec\) | \(W\) |
\( \rho \) (Greek symbol rho) = Fluid Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
\( n \) = Impeller Rotational Speed | \(rev \;/\; sec\) | \(rev \;/\; s\) |
\( d \) = Impeller Diameter | \(in\) | \(mm\) |
Power number, abbreviated as \(N_p\), a dimensionless number, represents the proportional drag force and inertial force. It is used in momentum transfer and power consumption by fans, mixers and pump impellers at a specified rotational speed. The power number formula depends on the geometry of the impeller, the Reynolds number of the flow, and the physical properties of the fluid. The value of the power number depends on the impeller design and the physical properties of the fluid, such as viscosity and surface tension. The power number is commonly used in the design and optimization of mixing processes, such as in chemical and biochemical reactors, fermentation vessels, and wastewater treatment systems.