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Circular weirAtmospheric pressure given altitudeHazen-Williams equation head lossAir specific massDynamic viscosity of atmospheric airErgun equation

Ergun equation

The Ergun equation is used to calculate pressure loss in porous media. This method takes into account the characteristics of the flow and particles to determine the resistance the fluid encounters as it moves through the medium.

The Ergun equation is expressed as follows:

$\frac{\Delta P}{L} = \frac{150 \mu (1 - \epsilon)^2}{d_p^2 \epsilon^3} \cdot \frac{q}{A} + \frac{1.75 \rho (1 - \epsilon)}{d_p \epsilon^3} \cdot \left(\frac{q}{A}\right)^2$

Where:

- $\Delta P$ is the pressure drop
- $L$ is the length of the porous bed
- $\mu$ is the fluid viscosity
- $\epsilon$ is the porosity of the medium
- $d_p$ is the average particle diameter
- $q$ is the volumetric flow rate
- $A$ is the cross-sectional area
- $\rho$ is the fluid density

Parameter | Default Units | Description |
---|---|---|

Volumetric flow ($q$) | - | Flow rate through the medium |

Specific mass ($\rho$) | kg/m³ | Fluid density |

Porosity ($\epsilon$) | - | Fraction of volume that is pore space |

Diameter of the particles ($d_p$) | m | Average size of the particles |

Viscosity ($\mu$) | Pa.s | Fluid's resistance to flow |

Sphericity | - | Measure of the shape of the particles |

Bed length ($L$) | m | Length of the porous medium |

Parameter | Default Units | Description |
---|---|---|

Pressure loss ($\Delta P$) | Pa | Pressure drop across the porous medium |

The Ergun equation is used to calculate pressure loss in porous media. This method takes into account the characteristics of the flow and particles to determine the resistance the fluid encounters as it moves through the medium.

The Ergun equation is expressed as follows:

$\frac{\Delta P}{L} = \frac{150 \mu (1 - \epsilon)^2}{d_p^2 \epsilon^3} \cdot \frac{q}{A} + \frac{1.75 \rho (1 - \epsilon)}{d_p \epsilon^3} \cdot \left(\frac{q}{A}\right)^2$

Where:

- $\Delta P$ is the pressure drop
- $L$ is the length of the porous bed
- $\mu$ is the fluid viscosity
- $\epsilon$ is the porosity of the medium
- $d_p$ is the average particle diameter
- $q$ is the volumetric flow rate
- $A$ is the cross-sectional area
- $\rho$ is the fluid density

Parameter | Default Units | Description |
---|---|---|

Volumetric flow ($q$) | - | Flow rate through the medium |

Specific mass ($\rho$) | kg/m³ | Fluid density |

Porosity ($\epsilon$) | - | Fraction of volume that is pore space |

Diameter of the particles ($d_p$) | m | Average size of the particles |

Viscosity ($\mu$) | Pa.s | Fluid's resistance to flow |

Sphericity | - | Measure of the shape of the particles |

Bed length ($L$) | m | Length of the porous medium |

Parameter | Default Units | Description |
---|---|---|

Pressure loss ($\Delta P$) | Pa | Pressure drop across the porous medium |

- Fonte: AZEVEDO NETTO, J. M. de; FERNANDEZ Y FERNANDEZ, Miguel. Manual de hidráulica, 9.ed. São Paulo: Blucher, 2015.