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Bevel-edged orifice in a straight pipe

Bevel-edged orifice in a straight pipe d d o ψ l
Bevel-edged orifice in a straight pipe

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} $
$ \{ψ\in\mathbb{R}\mid ψ>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.
$ ψ $ $ \mathrm{°} $
$ \{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} $

Calculation

Diameter ratio

$$β=\cfrac{d_o}{d}$$
$β=\cfrac{d_o}{d}$
Equations in LaTeX code
β=\cfrac{d_o}{d}
$$β\le\cfrac{1}{1+2\cdot\cfrac{l}{d_o}\cdot\tan{ψ}}$$
$β\le\cfrac{1}{1+2\cdot\cfrac{l}{d_o}\cdot\tan{ψ}}$
Equations in LaTeX code
β\le\cfrac{1}{1+2\cdot\cfrac{l}{d_o}\cdot\tan{ψ}}

Coefficient $ C_b $

$$C_b=\left(1-\cfrac{ψ}{90}\right)\cdot\left(\cfrac{ψ}{90}\right)^{\cfrac{1}{2+l/d_o}}$$
$C_b=\left(1-\cfrac{ψ}{90}\right)\cdot\left(\cfrac{ψ}{90}\right)^{\cfrac{1}{2+l/d_o}}$
Equations in LaTeX code
C_b=\left(1-\cfrac{ψ}{90}\right)\cdot\left(\cfrac{ψ}{90}\right)^{\cfrac{1}{2+l/d_o}}

Jet contraction ratio

$$λ=1+0.622\cdot\left[1-C_b\cdot\left(\cfrac{l}{d_o}\right)^{\cfrac{1-\sqrt[4]{l/d_o}}{2}}\right]\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$$
$λ=1+0.622\cdot\left[1-C_b\cdot\left(\cfrac{l}{d_o}\right)^{\cfrac{1-\sqrt[4]{l/d_o}}{2}}\right]\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$
Equations in LaTeX code
λ=1+0.622\cdot\left[1-C_b\cdot\left(\cfrac{l}{d_o}\right)^{\cfrac{1-\sqrt[4]{l/d_o}}{2}}\right]\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)

Loss coefficient

$$ζ=0.0696\cdot\left(1-C_b\cdot\cfrac{l}{d_o}\right)\cdot\left(1+0.42\cdot\sqrt{\cfrac{l}{d_o}}\cdot β^2\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2$$
$ζ=0.0696\cdot\left(1-C_b\cdot\cfrac{l}{d_o}\right)\cdot\left(1+0.42\cdot\sqrt{\cfrac{l}{d_o}}\cdot β^2\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2$
Equations in LaTeX code
ζ=0.0696\cdot\left(1-C_b\cdot\cfrac{l}{d_o}\right)\cdot\left(1+0.42\cdot\sqrt{\cfrac{l}{d_o}}\cdot β^2\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^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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