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Conical contraction

Conical contraction d 2 d 2 d 1 α
Conical 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{°} $
$ \{f\in\mathbb{R}\mid f>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.
$ f $

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}

Jet contraction ratio

$$λ=1+0.622\cdot\left(α/180\right)^{4/5}\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)$$
$λ=1+0.622\cdot\left(α/180\right)^{4/5}\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)$
Equations in LaTeX code
λ=1+0.622\cdot\left(α/180\right)^{4/5}\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)

Friction loss

$$K_{fr2}=\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}$$
$K_{fr2}=\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}$
Equations in LaTeX code
K_{fr2}=\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}

Local loss

$$K_{com2}=0.0696\cdot\sin{\left(α/2\right)}\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$$
$K_{com2}=0.0696\cdot\sin{\left(α/2\right)}\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$
Equations in LaTeX code
K_{com2}=0.0696\cdot\sin{\left(α/2\right)}\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2

Loss coefficient

$$ζ=K_{fr2}+K_{com2}$$
$ζ=K_{fr2}+K_{com2}$
Equations in LaTeX code
ζ=K_{fr2}+K_{com2}

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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