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Thick-edged orifice in a transition section

Thick-edged orifice in a transition section t d 2 d 1 d o
Thick-edged orifice in a transition section

Values for calculation

$d_1$ $\mathrm{mm}$
$d_2$ $\mathrm{mm}$
$d_o$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$f$

Calculation

Diameter ratio

$$β=\cfrac{d_o}{d_1}$$

Coefficient $ C_{th} $

$$C_{th}=\left[1-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^{2.5}-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^3\right]^{4.5}$$

Jet contraction ratio

$$λ=1+0.622\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$$

Loss coefficient

$\text{if }\ t/d_o\le 1.4$
$$ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+C_{th}\cdot\left(λ-\left(\cfrac{d_o}{d_2}\right)^2\right)^2+\left(1-C_{th}\right)\cdot\left[\left(λ-1\right)^2+\left(1-\left(\cfrac{d_o}{d_2}\right)^2\right)^2\right]$$
$\text{else}$
$$ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2+\left(1-\left(\cfrac{d_o}{d_2}\right)^2\right)^2+f\cdot\left(\cfrac{t}{d_o}-1.4\right)$$

Discharge coefficient

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$