## 2 Development of the Controlled Cutting Fluid Impinging Supply System (Cut-List)
### Theoretical Work
#### 2.2.2 Determination of Nozzle Aperture Diameter and Impinged Fluid Velocity  
The simplified version of [PERSON]'s equation was utilised to determine the relationship between pressure and velocity taking into consideration the cutting fluid specific gravity as shown in Equation (5) [44,59]. Also, at a given flow rate and impinging cutting fluid velocity, the exit circular area of coherent round nozzle A can be computed using the continuity Equation (6) [59]. Fluid velocities and the minimal required nozzle aperture diameters that fulfil the above-mentioned equations were computed. Pressures were measured by the digital pressure gauge at given flow rates resulting from Equation (6), and results are shown in Table 4.  
\[\Delta P=\frac{SG\times V\hat{j}^{2}}{535824} \tag{5}\]  
\[A=\frac{19.25\times Q_{n}}{CD\times V\hat{j}} \tag{6}\]  
To fulfil the flow coherency criterion, the contraction ratio (\(D/d\)) should be at least \(\geq\)2:1 and the actual nozzle aperture diameter (\(d\)) must be \(\geq\) the theoretical minimal coherent nozzle aperture diameter (\(d_{min}\)) in order to ensure the delivery of the required amount of cutting fluid [59]. For achieving the highest jet stream quality, the actual nozzle aperture diameter (\(d\)) was fixed at 1.75 mm for all trials, whereas the contraction ratio was set at about 6.85:1 based on the calculated  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Cutting Fluid** & **Impinged Fluid** & **Fluid Specific** & **Minimal Nozzle Aperture** & **Accurate Flow** \\
**Pressure (bars)** & **Velocity (m/s)** & **Gravity** & **Diameter – \(d_{min}\) (mm)** & **Rate (L/min)** \\ \hline
0.34 & 5.86 & 0.988 & 1.42 & 1 \\
0.55 & 7.46 & 0.988 & 1.50 & 1.5 \\
0.78 & 8.88 & 0.988 & 1.62 & 2.1 \\
1.16 & 10.83 & 0.988 & 1.75 & 3.1 \\ \hline \end{tabular}
\end{table}
Table 4: Results of the minimal nozzle apertures diameters and impinged fluid velocities.  
\begin{table}
\begin{tabular}{c c c} \hline
**Inputs** & **Corresponding Value** \\ \hline Cutting speed (m/min) & 95, 200 \\ Feed rate (mm/rev) & 0.1, 0.15 \\ Axial and radial depth of cut (mm) & 5, 1.3 \\ Cutting length (mm) & 103 \\ Specific cutting energy (W.s/mm\({}^{3}\)) & 4 [56] \\ Cutter diameter (mm) & 18.5 \\ Number of inserts & 1 \\ Compensation factor (K\({}_{1}\)) & 1.96 [57] \\ Inozzle & 0.95 \\ \(\Delta\theta\) (\({}^{\circ}\)C) & 2 [58] \\ \(\rho\) fluid mass density at 10\% concentration ratio (g/m\({}^{3}\)) & 0.988 \\ \(C\) fluid specific heat at 10\% concentration ratio (cal/g.\({}^{\circ}\)C) & 0.948 \\ \hline \end{tabular}
\end{table}
Table 2: Working conditions and values used for accurate flow rate calculations.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Cutting Speed** & **Feed Rate** & **Heat Generated** & \multicolumn{2}{c}{**Calculated Flow Rate (L/min)**} \\
**(m/min)** & **(mm/rev)** & **(kW)** & **Cut-list** & **Conventional System** \\ \hline
95 & 0.1 & 0.124 & 1 & 1.6 \\
95 & 0.15 & 0.187 & 1.5 & 2.4 \\
200 & 0.1 & 0.262 & 2.1 & 3.4 \\
200 & 0.15 & 0.393 & 3.1 & 5.2 \\ \hline \end{tabular}
\end{table}
Table 3: Flow rate results for the two systems.  
nozzle aperture diameter (i.e., 1.75 mm) and the given nozzle internal feed pipe diameter (i.e., 12 mm) which satisfy the flow coherency criterion.