## 3 Influence Factor Analysis for Water Jet Slotting Depth
### Jet Pressure  
The relationship between the jet pressure and the jet velocity is expressed by Equation (7). As can be seen, the jet pressure determines the jet velocity and impact energy, and thus affects the slotting  
Figure 2: (**a**) Axial velocity and (**b**) axial dynamic pressure of a water jet with different nozzle diameters [28].  
depth. To obtain the effect of jet pressure on the slotting depth, water jet cutting experiments were conducted with different jet pressures.  
\[v=\varphi\sqrt{\frac{2P}{\rho_{w}}}, \tag{7}\]  
where \(P\) is the jet velocity and \(\varphi\) is the nozzle velocity coefficient.  
The cutting experiment was conducted on an independently designed and developed water jet test system in the Laboratory of High-pressure Water Jets at Chongqing University, China. The system mainly consisted of a high-pressure pump, pressure and flow control system, and water jet test platform, as shown in Figure 3. The high-pressure pump, manufactured by Nanjing Luhe Coal Mine Machinery Co., Ltd., had a rated pressure of 56 MPa and rated flow rate of 200 L/min. The pressure-flow control system consisted of a pressure sensor of 0-70 MPa with a precision of \(\pm\)0.1% and an ultrasonic flowmeter of 0.5-20 m/s \(\pm\) 1%. Additionally, it was convenient to adjust the system pressure and monitor and record the pressure and flow at different times. The water jet test platform was comprised of a translation console and rock bearing system. The translation console had a translational speed of 0.01-1 m/s, and the rock bearing system, with an ultimate bearing weight of 5 t, could move up, down, forward, and backward. Moreover, the nozzle diameter and standoff distance were 3 and 165 mm, respectively. The translation speed was set to a constant of 0.12 m/s. Although it was very difficult to obtain coal blocks with large sizes, the coal block easily split when impacted by the water jet, owing to the typical anisotropy and abundant joints and fissures in the coal. This made it difficult to quantitatively evaluate the jet cutting efficiency. Besides, shaped coal of certain proportions has similar physical and mechanical properties, such as the compressive strength, tensile strength, and Poisson's ratio, of raw coal. It can well reflect the internal relationship between water jet parameters and rock-breaking efficiency of coal in the experiment [29; 30]. Therefore, shaped coals of size \(200\times 200\times 200\) mm were used as the cutting targets because they were adequately similar to coal; the f coefficient was 0.69.  
The cutting experiment results are presented in Figure 4. And the relationship between the jet pressure and the cutting depth can be obtained as shown in Figure 5. When the jet pressure was low, the cutting depth was shallow and approximately equal to zero because the jet pressure was lower than the critical rock-breaking pressure of the water jet. As the jet pressure increased, the cutting depth gradually increased, and the sample was completely cut through at a jet pressure of 22 MPa.  
Figure 3: System used in cutting experiment.  
As can be seen from the fitting curve, the cutting depth linearly increased with the jet pressure. Therefore, the relationship between the jet pressure and the cutting depth can be expressed as follows:  
\[h_{P}=k_{1}(P-P_{c}), \tag{8}\]  
where \(h_{P}\) is the cutting depth under different jet pressures; \(k_{1}\) is the proportionality coefficient; and \(P\) and \(P_{c}\) are the jet pressure and critical rock-breaking pressure, respectively. The critical rock-breaking pressure could show the effect of the coal strength on slotting depth to a certain extent.