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Round-edged orifice

Round-edged orifice d d o r
Round-edged orifice

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_o\in\mathbb{R}\mid d_o>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_o $ $ \mathrm{mm} $
$ \{r\in\mathbb{R}\mid r>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 $ $ \mathrm{mm} $

Calculation

Jet contraction ratio

$$λ=1+0.622\cdot\left(1-0.3\cdot\sqrt{\cfrac{r}{d_o}}-0.7\cdot\cfrac{r}{d_o}\right)^4$$
$λ=1+0.622\cdot\left(1-0.3\cdot\sqrt{\cfrac{r}{d_o}}-0.7\cdot\cfrac{r}{d_o}\right)^4$
Equations in LaTeX code
λ=1+0.622\cdot\left(1-0.3\cdot\sqrt{\cfrac{r}{d_o}}-0.7\cdot\cfrac{r}{d_o}\right)^4

Loss coefficient

$\text{if }\ r/d_o\geq 1$
$\text{if }\ r/d_o\geq 1$
Equations in LaTeX code
\text{if }\ r/d_o\geq 1
$$ζ=0.0696\cdot\left(1-0.569\right)+\left(1-\left(\cfrac{d_o}{d}\right)^2\right)^2$$
$ζ=0.0696\cdot\left(1-0.569\right)+\left(1-\left(\cfrac{d_o}{d}\right)^2\right)^2$
Equations in LaTeX code
ζ=0.0696\cdot\left(1-0.569\right)+\left(1-\left(\cfrac{d_o}{d}\right)^2\right)^2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_o}\right)\cdot λ^2+\left(λ-\left(\cfrac{d_o}{d}\right)^2\right)^2$$
$ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_o}\right)\cdot λ^2+\left(λ-\left(\cfrac{d_o}{d}\right)^2\right)^2$
Equations in LaTeX code
ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_o}\right)\cdot λ^2+\left(λ-\left(\cfrac{d_o}{d}\right)^2\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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