## 3 Results and Discussion
### Theoretical Calculations of Product Movement in the Screw Press  
The equations describing the movement of raw materials are compiled, and their solutions are proposed. The continuity equation for the steady fluid motion \(\frac{d\rho}{dt}=0\) is as follows:  
\(div\overset{\rightarrow}{v}=0\) or  
\[\frac{\partial v_{x}}{\partial x}+\frac{\partial v_{y}}{\partial y}+\frac{ \partial v_{z}}{\partial z}=0, \tag{6}\]  
For an incompressible fluid \(div\overset{\rightarrow}{v}=0\), the equations of the motion of a viscous fluid are described by the Navier-Stokes equation [39; 40]. \[\frac{d\overset{\rightarrow}{v}}{dt}=F-\frac{1}{\rho}grad\overset{ \rightarrow}{p}+\
u\Delta\overset{\rightarrow}{v}, \tag{7}\]  
Accordingly, according to Figure 18a,b, we consider the acting pressure forces along the \(x\), \(y\), \(z\) axes before and after grinding. Accordingly, since the surface of the uncrushed product is curvilinear (Figure 18a), during the pressing process, the forces form a system of non-parallel forces, and the force \(dF\) is divided into components [41]:  
\[\left. \begin{array}{l}dF_{x}=p_{x}dS\cos\alpha\\ dF_{y}=p_{y}dS\cos\beta\\ dF_{z}=p_{z}dS\cos\gamma\end{array} \right\}, \tag{8}\]  
where \(\alpha\), \(\beta\), \(\gamma\)--angles of inclination of elementary forces to coordinate axes, which are different for different sites \(dS\). Figure 17: Dependence of temperature of seed cake on the degree of sunflower seed grinding and screw rotation speed (different letters above the lines indicate significant differences between samples, \(p\) < 0.05). Accordingly, if we take into account all acting forces on the new surfaces of the product after grinding (Figure 18b) and determine the pressure on these surfaces, it is necessary to find the corresponding projections of the equal force:  
\[ \begin{array}{c}f_{x}=\sum p_{x}dS\cos\alpha\\ f_{y}=\sum p_{y}dS\cos\beta\\ f_{z}=\sum p_{z}dS\cos\gamma\end{array} \Biggr{\}}, \tag{9}\]  
From here, \(f=\sqrt{f_{x}^{2}+f_{y}^{2}+f_{z}^{2}}\), where \(\cos\alpha=\frac{f_{z}}{f}\), \(\cos\beta=\frac{f_{y}}{f}\), \(\cos\gamma=\frac{f_{z}}{f}\). If the pressure \(p\) along the length of the channel \(l\) and with a variable radius \(r_{t}\) is equal to the pressure change \(\Delta p\), to solve the problem of the mechanics of the homogeneous medium on the basis of the first Equation (1) and taking into account the pressure forces \(f_{z}=\Delta p\cdot\cdot\cdot r_{t}\)\({}^{2}\), and the force acting on the side surface is equal to \(f_{mp}=\mu\frac{dv}{dz}\cdot 2\pi\cdot r_{t}\cdot l\), then the pressure drop can be written in the following form, kPa:  
\[\Delta p=\frac{B}{\exp(\alpha,n)H}F\Big{(}\frac{uv_{z}}{h}\Big{)}^{1-n}l\cdot k _{T}ctga, \tag{10}\]  
Here, it must be taken into account that the inclination angle \(tg\alpha=\left(\frac{h}{W}\right)^{1-n}\) of the ground product depends on the pitch \(W=S_{t}\cdot cos\alpha\). For fluids that follow the power law [42; 43], the velocity of the product in the channel (Figure 19) along the \(z\)-axis (m/s) will be expressed by the formula:  
\[v_{z}=\frac{r_{t}n}{1+3n}\left[\frac{r_{t}}{2\mu}\bigg{(}\frac{dp}{dz}\bigg{)} \right]^{\frac{1}{h}}, \tag{11}\]  
where \(r_{t}\)--internal radius of rotation of the screw channel, m.  
Figure 19: Geometrical scheme of a Zeer cylinder. Figure 18: Pressure forces acting before and after grinding. 1—outer surface of the sunflower seeds; 2—macro and micro capillaries consisting of the liquid phase; 3—new surfaces after the grinding process. Taking into account the effect of pressing pressure on the formation of fat capillaries on the surface of the product during the pressing process, based on the theory of [PERSON] [44; 45], we determine the volume flow rate of separated oil by the following equation, m\({}^{3}\)/s.