# Ergun equation for beds + rising fluid + potential energy

• maistral
In summary, the Ergun equation for beds is a mathematical equation used to describe the pressure drop and fluid flow through a packed bed of particles. It takes into account factors such as particle size, fluid velocity, and bed porosity. The equation includes a term for fluid velocity to account for rising fluid and indirectly considers potential energy. The Ergun equation is commonly used in fluid dynamics and chemical engineering research and has limitations such as assumptions and neglect of particle-particle interactions.
maistral
TL;DR Summary
Do I add the potential energy term?
I am quite familiar with the Ergun equation's formulation.

My question is, do I need to subtract the potential term ΔP/Δz = -ρg/gc after the Ergun equation's own ΔP/Δz , assuming that the fluid is to be pumped upward, from the bottom of the bed to the top of the bed? I was thinking it should be negative because the fluid is counteracting gravity (fluid is flowing upward), which means that the pressure drop is greater.

Thanks.

Yes, that needs to be included.

## 1. What is the Ergun equation?

The Ergun equation is a mathematical equation used to describe the pressure drop in a fluid flowing through a packed bed of particles. It takes into account the effects of both the fluid flow and the particles in the bed.

## 2. How does the Ergun equation account for rising fluid?

The Ergun equation includes a term for the fluid velocity, which takes into account the rising motion of the fluid. This term is multiplied by the fluid density to account for the potential energy of the rising fluid.

## 3. What is the significance of potential energy in the Ergun equation?

Potential energy is included in the Ergun equation to account for the vertical movement of the fluid in a packed bed. This is important because it affects the pressure drop and overall flow behavior of the system.

## 4. Can the Ergun equation be applied to all types of beds and fluids?

While the Ergun equation is commonly used for packed beds and gases, it can also be applied to other types of beds and fluids. However, it may require modifications to account for different flow conditions or properties of the fluid and bed particles.

## 5. How is the Ergun equation derived?

The Ergun equation is derived from the Navier-Stokes equations, which describe the motion of a fluid. It also takes into account the properties of the bed particles, such as their size and shape, and the interactions between the fluid and particles.

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