1.3.3 Herschel Bulkley Model
The Herschel Bulkley model was introduced in 1926. Unlike the Bingham plastic model and the Power law model, which are both two parameter rheological models, the Herschel and Bulkley model is a three parameter rheological model. The Herschel-Bulkley equation is preferred to power law or Bingham relationships because it results in more accurate models of rheological behaviour when adequate experimental data are available. The graphical model derived from the arithmetic interpretation is called the Herschel-Bulkley model or the yield power law model as stated by [4]. The arithmetic equation of the Herschel Bulkley model is shown below.
\(\tau=\ \tau_{0}+\ \mu\ \ x\ \left(\gamma\right)^{n}\ \) (5)
\begin{equation} where,\ \tau\nonumber \\ \end{equation}\begin{equation} =shear\ stress\ of\ the\ fluid\ measured\ in\ \ \frac{\text{lb}}{100\text{ft}^{2}}\nonumber \\ \end{equation}\begin{equation} \tau_{0}=yield\ stress\ of\ the\ fluid\ measured\ in\ \frac{\text{lb}}{100\text{ft}^{2}}\ \nonumber \\ \end{equation}\begin{equation} n=power\ law\ exponent\ and\ flow\ index\ of\ the\ fluid\ \nonumber \\ \end{equation}\begin{equation} \gamma=fluid\ shear\ rate\ measured\ in\text{\ sec}^{-1}\ \nonumber \\ \end{equation}
\(\mu=\ \)Consistency index of the fluid measured in CP