$\alpha$	Coefficient of the velocity loss of the pure liquid jet in the interaction with material in a solid state (energetic coefficient) … (–)
${\alpha }_e$	Experimentally determined coefficient of the abrasive water jet velocity loss in the interaction with material … (–)
${\alpha }_n$	Coefficient of the velocity loss of the pure liquid jet in the interaction with material in a solid state after the n-th pass of the jet through the same trace … (–)
$\gamma$	Compressibility of the liquid for pressure $p_o$ … (Pa−1)
${\gamma }_o,{\gamma }_p$	Shortened expression $(1-\gamma p_o)$… (–)
$\eta$	Dynamic viscosity of the liquid … (N·s·m−2)
$\theta$	Tilting angle of the cutting head measured in the plane containing the vector of the traverse speed and stating the deviation of the jet axis and the perpendicular in the point where the jet axis penetrates the inlet surface of material … (rad or °)
$\vartheta$	Declination angle measured in the plane containing the vector of the traverse speed and stating the deviation of the tangent to the striation at the outlet surface of material and the inlet jet axis … (rad or °)
$\phi$	Inclination angle measured in the plane perpendicular to the plane containing the vector of the traverse speed and stating the deviation of the tangent to the side wall of the cut and the inlet jet axis … (rad or °)
$\chi$	Coefficient of the reflected liquid jet expansion due to the mixing with the disintegrated material (coefficient of the jet trace widening) … (–)
$\mu ,{\mu }_o$	Nozzle discharge coefficient … (–)
$\rho ,{\rho }_o$	Density of the liquid under the normal conditions … (kg·m−3)
${\rho }_a$	Density of the abrasive material … (kg·m−3)
${\rho }_j$	Density of the abrasive jet (conversion to homogeneous liquid) … (kg·m−3)
${\rho }_m$	Density of material being machined … (kg·m−3)
${\rho }_M$	Specific volume density of disintegrated material (including pores) … (kg·m−3)
${\rho }_M^{*}$	Specific mass density of the disintegrated material (excluding pores) … (kg·m−3)
$\sigma$	Strength of the target material (compressive, tensile or shear) … (Pa)
${\sigma }_m$	Strength of material being machined … (Pa)
${\sigma }_s$	Shear strength of the target material … (Pa)
$\xi$	Attenuation coefficient of the liquid jet between the nozzle outlet and the material surface … (m−1)
${\xi }^{*}$	Attenuation coefficient of the liquid jet in the already formed kerf … (m−1)
${\xi }_j$	Attenuation coefficient of abrasive jet in the environment between the focusing tube outlet and the material surface … (m−1)
$a$	Mean size of the element of material structure—the grain … (m)
$a_n$	Mean size of abrasive particles formed in the mixing process … (m)
$a_m$	Mean size of particles (elements) of material—grains or their chips … (m)
$a_o$	Mean size of abrasive particles entering the mixing process … (m)
$c$	Sound velocity inside the abrasive material … (m·s−1)
$c_o$	Sound velocity inside the liquid used for preparation of the abrasive liquid jet (usually water) … (m·s−1)
$C_f$	Friction coefficient of the liquid on the material element protruding to the jet flow … (–)
$C_1$	Coefficient modifying abrasive jet velocity in relation to the quantity of abrasive material input … (–)
$C_2$	Coefficient modifying abrasive jet velocity in relation to the ratio between the focusing tube diameter and the average abrasive particle size resulting from the mixing process … (–)
$C_3$	Coefficient modifying abrasive jet velocity in relation to the friction inside the focusing tube … (–)
$C_4$	Coefficient modifying abrasive jet velocity in relation to the focusing tube opening … (–)
$C_A$	Coefficient modifying abrasive water jet performance in relation to the changing content of abrasive below the so-called saturation level (above this level the jet performance increase is impossible and $C_A=1$) … (–)
$C_D$	Abrasive particle drag coefficient inside the liquid used for a preparation of the abrasive liquid jet (usually water) … (–)
$d_o$	Water nozzle diameter (usually called orifice diameter) … (m)
$d_a$	Focusing tube diameter … (m)
$D$	Resulting theoretical diameter of the outlet cylinder base of the sample cut by the abrasive water jet when the deformation caused by both the declination and the inclination angle is calculated … (m)
$D_{ie}$	Experimentally determined diameter of the cylindrical sample at the abrasive water jet inlet side … (m)
$D_{oe}$	Experimentally determined diameter of the cylindrical sample at the abrasive water jet outlet side … (m)
$D_{it}$	Diameter of the cylindrical sample at the abrasive water jet inlet side calculated from the presented theoretical model … (m)
$D_{ot}$	Diameter of the cylindrical sample at the abrasive water jet outlet side calculated from the presented theoretical model … (m)
$E_P$	Specific surface energy of the abrasive material … (J)
$f$	Friction coefficient of abrasive particle on the focusing tube wall … (–)
$h$	Depth of material disintegration (depth of cut) … (m)
$h_{lim}$	Maximum depth of liquid jet penetration into material for the selected conditions … (m)
$h_n$	Depth of disintegration for the n-th pass of the jet through the same trajectory on the material surface … (m)
$h_n^{*}$	Summary depth of the jet penetration into material after the n-th pass of the jet trace in the case of multiple passes through the same trajectory on the material surface … (m)
$H$	Material thickness … (m)
$HV$	(Vickers’) material hardness … (N·m−2)
$k^{*}$	“Dynamic” permeability of material … (m2)
$K$	Material hardness … (N·m−2)
$l_a$	Length of the focusing tube … (m)
$L$	Stand-off distance of the material surface or the investigated plane perpendicular to the liquid jet axis from the nozzle or the focusing tube outlet … (m)
$p_o$	Pressure of liquid before the nozzle (in the pump) … (Pa)
$p_j$	Pressure obtained from Bernoulli’s equation for a liquid with the density and the velocity of an abrasive jet … (Pa)
$q_a$	Abrasive mass flow rate … (kg·s−1)
$q_w$	Water mass flow rate … (kg·s−1)
$R$	Radius of the pre-set circle path of the jet axis intersection with surface of material plate from which the sample is cut … (m)
$S_P$	Ratio between the quantity of non-damaged grains (i.e., not containing defects) and the total quantity of grains in the abrasive water jet … (–)
$t_i$	Interaction time … (s)
$T$	Correction of the outlet edge of the sample caused by the taper angle … (m)
$v_a$	Abrasive jet speed after the mixing process … (m·s−1)
$v_i$	Water jet speed before the mixing process … (m·s−1)
$v_P$	Traverse speed of the jet trace on the material surface … (m·s−1)
${\tilde{v}}_P$	Traverse speed of the jet trace on the material surface modified by minimum traverse speed ($v_P+v_{Pmin}$) … (m·s−1)
$v_{Pmin}$	Minimum traverse speed of cutting—correction for the zero traverse speed (the value should be equal to the average mean size of the abrasive particles after the mixing process per minute, i.e., $v_{Pmin}=a_n/60$) … (m·s−1)
$v_{Plim}$	Limit traverse speed of the jet trace on the material surface calculated for the material thickness $H$… (m·s−1)
$v_{Ptilt}$	Traverse speed of the jet trace on the material surface calculated for compensation of the deformation caused by the outlet declination angle 20° … (m·s−1)
$v_{PQ}$	Traverse speed of the jet trace ensuring selected quality of cut walls … (m·s−1)