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Thick-edged orifice

Thick-edged orifice d d o t
Thick-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} $
$ \{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} $

Calculation

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}

Loss coefficient

$$ζ=0.183+C_{th}\cdot\left[1.622-\left(\cfrac{d_o}{d}\right)^2\right]^2+\left(1-C_{th}\right)\cdot\left\{0.387+\left[1-\left(\cfrac{d_o}{d}\right)^2\right]^2\right\}$$
$ζ=0.183+C_{th}\cdot\left[1.622-\left(\cfrac{d_o}{d}\right)^2\right]^2+\left(1-C_{th}\right)\cdot\left\{0.387+\left[1-\left(\cfrac{d_o}{d}\right)^2\right]^2\right\}$
Equations in LaTeX code
ζ=0.183+C_{th}\cdot\left[1.622-\left(\cfrac{d_o}{d}\right)^2\right]^2+\left(1-C_{th}\right)\cdot\left\{0.387+\left[1-\left(\cfrac{d_o}{d}\right)^2\right]^2\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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