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Multi-hole cage

Cage
Cage
Developed_view_of_the_cage
Developed view of the cage

Values for calculation

$Q_{max}$ $\mathrm{m^3/s}$
$D$ $\mathrm{mm}$
$D_c$ $\mathrm{mm}$
$P_1$ $\mathrm{Pa}$
$P_2$ $\mathrm{Pa}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_T$ $\mathrm{Pa}$
$μ_i$
$d_i$ $\mathrm{mm}$
$L$ $\mathrm{mm}$

Calculation

Velocity in valve

$$v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}$$

Allowable maximum number of holes in one row

$$n_{max}=\cfrac{π\cdot D_c}{\sqrt{\left(9\cdot d_i\right)^2-\left(3\cdot d_i\right)^2}}$$

The flow area

$$A=\cfrac{Q_{max}}{μ_i\cdot \sqrt{2\cdot \cfrac{P_1-P_2}{ρ}}}$$

Number of holes

$$I=\cfrac{4\cdot 10^6 \cdot A}{π\cdot d_i^2}$$

Requirements

$$\cfrac{P_1-P_2}{0.6\cdot\left(P_1-P_T\right)}\le1$$$$\cfrac{4\cdot 10^6\cdot A}{π\cdot D^2}<0.5$$$$\cfrac{D}{50}\geq d_i$$