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Pipe reducer

Pipe reducer α d 2 d 1 l
Pipe reducer

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} $
$ \{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} $
$ \{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

Angle

$$α=2\cdot\tan^{-1}{\left(\cfrac{d_2-d_1}{1.2\cdot l}\right)}\cdot\cfrac{180}{π}$$
$α=2\cdot\tan^{-1}{\left(\cfrac{d_2-d_1}{1.2\cdot l}\right)}\cdot\cfrac{180}{π}$
Equations in LaTeX code
α=2\cdot\tan^{-1}{\left(\cfrac{d_2-d_1}{1.2\cdot l}\right)}\cdot\cfrac{180}{π}

Diameter ratio

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

Loss coefficient

$$ζ=f\cdot\cfrac{0.2\cdot l}{d_1}+\cfrac{f\cdot\left(1-β\right)}{8\cdot\sin{\left(α/2\right)}}+f\cdot\cfrac{0.2\cdot l}{d_2}\cdot β^4$$
$ζ=f\cdot\cfrac{0.2\cdot l}{d_1}+\cfrac{f\cdot\left(1-β\right)}{8\cdot\sin{\left(α/2\right)}}+f\cdot\cfrac{0.2\cdot l}{d_2}\cdot β^4$
Equations in LaTeX code
ζ=f\cdot\cfrac{0.2\cdot l}{d_1}+\cfrac{f\cdot\left(1-β\right)}{8\cdot\sin{\left(α/2\right)}}+f\cdot\cfrac{0.2\cdot l}{d_2}\cdot β^4

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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