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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}}