Burke-Plummer equation

This is known as the Burke-Plummer equation and, as noted, applies for NRe,PM > 1000. 

This equation with a value of 150 instead of 180 is called the Ergun equation and is simply the sum of Eqs (13-15) and (13-16). (The more recent references favor the value of 180, which is also more conservative.) Obviously, for ARcRM < 10 the first term is small relative to the second, and the Ergun equation reduces to the Blake-Kozeny equation. Likewise, for A Re PM > 1000 the first term is much larger than the second, and the equation reduces to the Burke-Plummer equation. 

It was found experimentally that 3/ = 1.75. With this value, Equation (23) becomes known as the Burke Plummer equation ... 

Dalla Valle1 s Method—The author used an equation due to Burke and Plummer (1928) for determining the pressure-drop through packed columns. For streamline flow of air through packings of various sands in a 3 in. diameter column, the modified Burke-Plummer equation takes the form... 

These two frictional loss terms can be used in the mechanical energy balance, leading to the Blake-Kozeny equation (for low Re) and the Burke-Plummer equation (for higher Re). Ergun combined the two to give the most well-known equation for flow through packed beds ... 

For highly turbulent flow the friction factor should approach a constant value. Also, it is assumed that all packed beds should have the same relative roughness. Experimental data indicated that 3/= 1.75. Hence, the final equation for turbulent flow for > 1000, which is called the Burke-Plummer equation, becomes... 

Eq. (4.99) is the Burke—Plummer equation for turbulent flow through... 

The Blake-Kozeny equation and the Burke—Plummer equation define the limiting flow regimes for a fluid passing through a mass of spherical particles. Ergun added these equations to obtain... 

When the Blake-Kozeny equation for laminar flow and the Burke-Plummer equation for turbulent flow are simply added together, the result is... 

The Burke-Plummer equation is used to express the pressure drop for turbulent flow conditions (Re > 1000). For this condition, the result is ... 

Solution. Note that for high rates of flow, the first term on the right-hand side of the Ergun equation drops out and the equation reduces to the Burke-Plummer equation. At low rates of flow, the second term on the right-hand side drops out and the Blake-Kozeny equation is obtained. It should be emphasized that the Ergun equation is but one of many that have been proposed for describing the pressure drop across packed columns. For example, Theodore provide the following simple equation. 

Hardly surprisingly, the experimentally determined value for the constant in the above relation, 3f = 1.75, turns out to be orders of magnitude larger than is the case for tube flow. With this value, however, the relation provides a reasonable estimate of many reported observations, and becomes known as the Burke-Plummer equation. 

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