## 3 Results and Discussion
The \(\Delta P_{12}\) data were processed in the same way as the net pressure loss (\(\Delta P\)), to yield the following empirical correlations;  
\[\Delta P=\Delta P_{13}-\Delta P_{Ld} \tag{5}\]9  
\[\frac{\Delta P_{Ld}}{L_{Ld}}=\frac{4}{D}\bigg{(}\frac{8U}{D}\frac{24.27712 \phi_{s}{}^{2}+0.0861\phi_{s}-4}{32.3616\phi_{s}{}^{2}+0.1148\phi_{s}-4}\bigg{)} ^{(-8.0904\phi_{s}{}^{2}-0.0287\phi_{s}+1)}\exp\left(77.7250\phi_{s}{}^{2}-1.888 7\phi_{s}-5.0546\right) \tag{6}\]0  
\[\frac{\Delta P_{Ld}}{L_{Ld}}=\frac{4}{D}\bigg{(}\frac{8U}{D}\frac{24.27712 \phi_{s}{}^{2}+0.0861\phi_{s}-4}{32.3616\phi_{s}{}^{2}+0.1148\phi_{s}-4}\bigg{)} ^{(-8.0904\phi_{s}{}^{2}-0.0287\phi_{s}+1)}\exp\left(77.7250\phi_{s}{}^{2}-1.888 7\phi_{s}-5.0546\right) \tag{6}\]1 _Cont._  
\[\frac{\Delta P_{Ld}}{L_{Ld}}=\frac{4}{D}\bigg{(}\frac{8U}{D}\frac{24.27712 \phi_{s}{}^{2}+0.0861\phi_{s}-4}{32.3616\phi_{s}{}^{2}+0.1148\phi_{s}-4}\bigg{)} ^{(-8.0904\phi_{s}{}^{2}-0.0287\phi_{s}+1)}\exp\left(77.7250\phi_{s}{}^{2}-1.888 7\phi_{s}-5.0546\right) \tag{6}\]2 Reproduced solid volume fraction using Equation (14) for the 15 mm bore orifice. Figure 11 presents the reproduced solid volume fractions (\(\phi_{\rm s}^{\prime}\)) using Equation (15). The maximum error is 2.33 vol.%, and the standard error is 0.68 vol.% (less than 4.6% of the determined solid volume fraction). Figure 12 presents the reproduced solid volume fractions using Equation (16). The maximum error is 6.45 vol.%, and the standard error is 2.5 vol.%. The performance of Equation (15) is not inferior to that of Equation (13). \[\frac{\Delta P_{Ld}}{L_{Ld}}=\frac{4}{D}\bigg{(}\frac{8U}{D}\frac{24.27712 \phi_{s}{}^{2}+0.0861\phi_{s}-4}{32.3616\phi_{s}{}^{2}+0.1148\phi_{s}-4}\bigg{)} ^{(-8.0904\phi_{s}{}^{2}-0.0287\phi_{s}+1)}\exp\left(77.7250\phi_{s}{}^{2}-1.888 7\phi_{s}-5.0546\right) \tag{6}\]3 Reproduced solid volume fractions using Equation (15) for the 10 mm bore orifice. \[\frac{\Delta P_{Ld}}{L_{Ld}}=\frac{4}{D}\bigg{(}\frac{8U}{D}\frac{24.27712 \phi_{s}{}^{2}+0.0861\phi_{s}-4}{32.3616\phi_{s}{}^{2}+0.1148\phi_{s}-4}\bigg{)} ^{(-8.0904\phi_{s}{}^{2}-0.0287\phi_{s}+1)}\exp\left(77.7250\phi_{s}{}^{2}-1.888 7\phi_{s}-5.0546\right) \tag{6}\]4 Regression of pressure drop as a linear function of the solid volume fraction for the orifice bores of (**a**) 10 mm, and (**b**) 15 mm. It is concluded that the solid volume fraction of aqueous R134a hydrate slurry can be monitored using Equation (15) from the measured flow rate and pressure difference between 50 mm upstream and 100 mm downstream from the upstream face of the square-edged orifice having a bore of 10 mm. The uncertainty is less than 12% of the determined solid volume fraction, in which about 7.2% is the biased uncertainty in obtaining raw solid volume fraction data [contributions (1)-(3) to the uncertainty in the solid volume fraction, as discussed in the \"Experiments\"], while about 4.6% is the random error resulting from the regression process, in addition to contribution (4). A short span between pressure measuring locations is advisable to ease the complexity of facility layout design and cost constraints. Comparing to the other technologies, this method is non-destructive, cost effective and does not require frequent calibration.