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Thick-edged orifice in a straight pipe

Thick-edged orifice in a straight pipe d d o t
Thick-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} $
$ \{t\in\mathbb{R}\mid 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.
$ t $ $ \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

Diameter ratio

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

Coefficient $ C_{th} $

$$C_{th}=\left[1-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^{2.5}-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^3\right]^{4.5}$$
$C_{th}=\left[1-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^{2.5}-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^3\right]^{4.5}$
Equations in LaTeX code
C_{th}=\left[1-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^{2.5}-0.5\cdot\left(\cfrac{t}{1.4\cdot d_o}\right)^3\right]^{4.5}

Jet contraction ratio

$$λ=1+0.622\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$$
$λ=1+0.622\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$
Equations in LaTeX code
λ=1+0.622\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)

Loss coefficient

$\text{if }\ t/d_o\le 1.4$
$\text{if }\ t/d_o\le 1.4$
Equations in LaTeX code
\text{if }\ t/d_o\le 1.4
$$ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+C_{th}\cdot\left(λ-β^2\right)^2+\left(1-C_{th}\right)\cdot\left[\left(λ-1\right)^2+\left(1-β^2\right)^2\right]$$
$ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+C_{th}\cdot\left(λ-β^2\right)^2+\left(1-C_{th}\right)\cdot\left[\left(λ-1\right)^2+\left(1-β^2\right)^2\right]$
Equations in LaTeX code
ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+C_{th}\cdot\left(λ-β^2\right)^2+\left(1-C_{th}\right)\cdot\left[\left(λ-1\right)^2+\left(1-β^2\right)^2\right]
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2+\left(1-β^2\right)^2+f\cdot\left(\cfrac{t}{d_o}-1.4\right)$$
$ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2+\left(1-β^2\right)^2+f\cdot\left(\cfrac{t}{d_o}-1.4\right)$
Equations in LaTeX code
ζ=0.0696\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2+\left(1-β^2\right)^2+f\cdot\left(\cfrac{t}{d_o}-1.4\right)

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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