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Discharge from a round-edged orifice

Discharge from a round-edged orifice d r d o
Discharge from a 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

Diameter ratio

$$β=\cfrac{d_o}{d}$$
$β=\cfrac{d_o}{d}$
Equations in LaTeX code
β=\cfrac{d_o}{d}

Jet contraction ratio

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

Loss coefficient

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