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Flow nozzle

Flow nozzle d d T r 1 r 2 l T
Flow nozzle

Values for calculation

$ \{d\in\mathbb{R}\mid d>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 $ $ \mathrm{mm} $
$ \{d_T\in\mathbb{R}\mid d_T>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_T $ $ \mathrm{mm} $
$ \{r_1\in\mathbb{R}\mid r_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.
$ r_1 $ $ \mathrm{mm} $
$ \{r_2\in\mathbb{R}\mid r_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.
$ r_2 $ $ \mathrm{mm} $
$ \{f_T\in\mathbb{R}\mid f_T>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_T $
$ \{l_T\in\mathbb{R}\mid l_T>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_T $ $ \mathrm{mm} $

Calculation

Radius

$$r=\sqrt[3]{r_1^2\cdot r_2}$$
$r=\sqrt[3]{r_1^2\cdot r_2}$
Equations in LaTeX code
r=\sqrt[3]{r_1^2\cdot r_2}
$$r/d_T< 1$$
$r/d_T< 1$
Equations in LaTeX code
r/d_T< 1

Diameter ratio

$$β=d_T/d$$
$β=d_T/d$
Equations in LaTeX code
β=d_T/d

Jet contraction ratio

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

Loss coefficient

$$ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_T}\right)\cdot\left(1-\sqrt{\cfrac{r}{d_T}}\cdot β\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2+f_T\cdot\cfrac{l_T}{d_T}$$
$ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_T}\right)\cdot\left(1-\sqrt{\cfrac{r}{d_T}}\cdot β\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2+f_T\cdot\cfrac{l_T}{d_T}$
Equations in LaTeX code
ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_T}\right)\cdot\left(1-\sqrt{\cfrac{r}{d_T}}\cdot β\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2+f_T\cdot\cfrac{l_T}{d_T}

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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