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Elliptical rounded contraction

Elliptical rounded contraction d 2 d 1 r 1 r 2
Elliptical rounded contraction

Values for calculation

$d_1$ $\mathrm{mm}$
$d_2$ $\mathrm{mm}$
$r_1$ $\mathrm{mm}$
$r_2$ $\mathrm{mm}$

Calculation

Radius

$$r=\sqrt[3]{r_1^2\cdot r_2}$$

Diameter ratio

$$β=\cfrac{d_2}{d_1}$$

Jet contraction ratio

$$λ=1+0.622\cdot\left(1-0.3\cdot\sqrt{\cfrac{r}{d_2}}-0.7\cdot\cfrac{r}{d_2}\right)^4\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$$

Loss coefficient

$\text{if }\ r/d_2\geq 1$
$$ζ=0.03\cdot\left(1-β\right)\cdot\left(1-β^4\right)$$
$\text{else}$
$$ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_2}\right)\cdot\left(1-\sqrt{\cfrac{r}{d_2}}\cdot β\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$$

Discharge coefficient

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$