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Beveled contraction

Beveled contraction d 2 d 2 d 1 l α/2
Beveled contraction

Values for calculation

$ \{d_1\in\mathbb{R}\mid d_1>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ d_1 $ $ \mathrm{mm} $
$ \{d_2\in\mathbb{R}\mid d_2>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ d_2 $ $ \mathrm{mm} $
$ \{α\in\mathbb{R}\mid α>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ α $ $ \mathrm{°} $
$ \{l\in\mathbb{R}\mid l>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ l $ $ \mathrm{mm} $

Calculation

Diameter ratio

$$β=\cfrac{d_2}{d_1}$$
$β=\cfrac{d_2}{d_1}$
Equations in LaTeX code
β=\cfrac{d_2}{d_1}

Coefficient $ C_B $

$$C_B=\cfrac{l}{d_2}\cdot\cfrac{2\cdot β\cdot\tan{\left(α/2\right)}}{1-β}$$
$C_B=\cfrac{l}{d_2}\cdot\cfrac{2\cdot β\cdot\tan{\left(α/2\right)}}{1-β}$
Equations in LaTeX code
C_B=\cfrac{l}{d_2}\cdot\cfrac{2\cdot β\cdot\tan{\left(α/2\right)}}{1-β}

Jet contraction ratio

$$λ=1+0.622\cdot\left[1+C_B\cdot\left(\left(\cfrac{α}{180}\right)^{0.8}-1\right)\right]\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)$$
$λ=1+0.622\cdot\left[1+C_B\cdot\left(\left(\cfrac{α}{180}\right)^{0.8}-1\right)\right]\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)$
Equations in LaTeX code
λ=1+0.622\cdot\left[1+C_B\cdot\left(\left(\cfrac{α}{180}\right)^{0.8}-1\right)\right]\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)

Loss coefficient

$$ζ=0.0696\cdot\left[1+C_B\cdot\left(\sin{\left(α/2\right)}-1\right)\right]\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$$
$ζ=0.0696\cdot\left[1+C_B\cdot\left(\sin{\left(α/2\right)}-1\right)\right]\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$
Equations in LaTeX code
ζ=0.0696\cdot\left[1+C_B\cdot\left(\sin{\left(α/2\right)}-1\right)\right]\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2

Discharge coefficient

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$
$μ=\cfrac{1}{\sqrt{ζ+1}}$
Equations in LaTeX code
μ=\cfrac{1}{\sqrt{ζ+1}}
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