HAALAND equation

The Haaland equation provides a useful approximation that does not require iteration ... 

Problem Statement Use the Colebrook and Haaland equations to calculate the friction factor with e/D = 0.008 and Re = 8 X 10 . 

Solution We begin with the Haaland equation, as it does not require any iteration. This gives... 

Thus, the Haaland equation is a bit more than 3% too high. This is well within the accuracy of the calculation indeed, the relative roughness is never known with certainty and can change with use. 

The Colebrook equation is implicit inf, and thus the determination of the friction factor requires some iteration unless an equation solver such as EES is used. All approximate explicit relation for/was given by S. E. Haaland in 1983 as... 

David Haaland et al. added to the modeling literature with a 1992 paper [9]. This work used whole blood for the model. Scanning from 1500 to 2400 nm, a PLS equation was developed on glucose-spiked whole blood. The range between 0.17 and 41.3 mM yielded an equation with a standard error of 1.8 mM. Four patients were used as models for this project. Cross-validated PLS standard errors for glucose concentration based on data obtained from all four subjects were 2.2 mM. 

It is interesting to compare Allinger s results with Rm calculated from the available interatomic distances in of MXn molecules by Eq. 4.20, depending significantly on the M-X bond polarity. This dependence was described in [53] by an equation, similar to that suggested earlier (but for different purposes) by Blom and Haaland... 

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