## 3 Results and Discussion
### Physical Modeling of the Process of Centrifugation of Meat-Bone Cracklings
#### 3.2.2 Deriving the 2 nd Criterion Equation  
The centrifugal pressure generated in the centrifuge was used to form the sludge and move the cleared liquid (fugate) through the openings in the drum body [29; 30]. Excess elementary pressure of centrifugal force \(dp\):  
\[dp=\frac{dP}{F}=\frac{M\omega^{2}dr}{\pi DH} \tag{13}\]  
where  
\(dp\)--elementary centrifugal force, N;  
\(F\)--area of the inner side surface of the centrifuge drum, m\({}^{2}\);  
\(M\)--mass of slurry in the drum, kg;  
\(\omega\)--angular rotation speed, s\({}^{-1}\);  
\(dr\)--elementary radius of the drum, m;  
\(D\)--inner diameter of drum, m;  
\(H\)--height of slurry level in the drum, m.  
This excess elemental pressure was applied to the filtering process:  
\[dp=du\cdot R \tag{14}\]  
where  
\(du\)--elementary speed of filtered suspension, m\({}^{3}\);  
\(R\)--total resistance of sludge and perforation holes, kg/s\(\cdot\)m\({}^{2}\); (the numerical value is selected from reference tables or calculated).  
By equating Equation (13) to (14), we obtain the centrifugal filtration Equation (15):  
\[dp=\frac{\mathrm{M}\omega^{2}dr}{\pi DH}=du\cdot R \tag{15}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Centrifuge** & **Optimal** & **Loading of** & **Reynolds** & **Parameter** & **Degree** & **Specific Calculated** & **Maximum** \\
**Rotor Rotational** & **Configuration** & **Tine** & **into the** & **Number** & **(kg/m\({}^{2}\)-s)** & **Coefficient** & **Degree** & **Yield of Meat-Bone** & **Production Capacity** \\
**Speed** & **Time** & **Centrifuge** & **Re\({}_{cf}\)** & **\(\rho\cdotp\cdotp\)** & **\(B\)** & **Index,** & **Crackings in** & **of the Squash,** \\
**n, rpm** & **\(\tau\), min** & **G\({}_{v}\), g** & **\(\rho\cdotp\cdotp\)** & **\(B\)** & **\(K=-x\)** & **kg/s\({}^{-1}\)m\({}^{2}\)** & **g/min** \\ \hline
1000 & 5 & 880 & 38,507 & 2995.0 & 1.73 & 1.155 & 0.0262 & 100.02 \\ \hline
1500 & 5 & 870 & 56,989 & 4432.5 & 1.73 & 1.155 The differentiation symbols are crossed out and converted for the steady-state equilibrium process of centrifugal filtration:  
\[p=\frac{\text{M}\omega^{2}r}{\pi\text{DH}}=u\cdot R \tag{16}\]  
\[\frac{\text{M}\omega^{2}r}{\pi\text{DH}\cdot u\cdot R}=\frac{P}{R_{\Sigma}}=K_{ \text{cf}}=1 \tag{17}\]  
\[\frac{P}{R_{\Sigma}}=K_{\text{cf}}=1 \tag{18}\]  
We obtained a dimensionless complex, \(K_{\text{cf}}\), which characterizes the balance of the ratio of centrifugal force to filtration resistance force during the flow of suspension through capillaries at the steady-state centrifugation process.  
\(P=M\cdot\omega^{2}\cdot R\)--centrifugal force, N.  
\(R_{\Sigma}\)--is the total force of resistance to centrifugal filtration, N.  
\(R_{\Sigma}=\pi\text{DH}\cdot u\cdot R\)  
\(K_{\text{cf}}\)--criterion for balanced centrifugal filtration.  
It is often necessary to calculate the average centrifugal filtration velocity (\(u\)), which is determined from Equation (16):  
\[u=\frac{\text{M}\omega^{2}r}{\pi\text{DH}R} \tag{19}\]  
or in a criterion form:  
\[u=K^{-1}\text{cf}\frac{\text{M}\omega^{2}r}{\pi\text{DH}\cdot R} \tag{20}\]