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