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Curved wall diffuser

Curved wall diffuser d 2 d 1 l
Curved wall diffuser

Values for calculation

$ \{d_1\in\mathbb{R}\mid d_1>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_1 $ $ \mathrm{mm} $
$ \{d_2\in\mathbb{R}\mid d_2>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_2 $ $ \mathrm{mm} $
$ \{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

$$β=\cfrac{d_1}{d_2}$$
$β=\cfrac{d_1}{d_2}$
Equations in LaTeX code
β=\cfrac{d_1}{d_2}
$$0.1< β^2< 0.9$$
$0.1< β^2< 0.9$
Equations in LaTeX code
0.1< β^2< 0.9

Coefficient $ φ_0 $

$$φ_0=1.01-0.624\cdot\cfrac{l}{d_1}+0.3\cdot\left(\cfrac{l}{d_1}\right)^2-0.074\cdot\left(\cfrac{l}{d_1}\right)^3+0.007\cdot\left(\cfrac{l}{d_1}\right)^4$$
$φ_0=1.01-0.624\cdot\cfrac{l}{d_1}+0.3\cdot\left(\cfrac{l}{d_1}\right)^2-0.074\cdot\left(\cfrac{l}{d_1}\right)^3+0.007\cdot\left(\cfrac{l}{d_1}\right)^4$
Equations in LaTeX code
φ_0=1.01-0.624\cdot\cfrac{l}{d_1}+0.3\cdot\left(\cfrac{l}{d_1}\right)^2-0.074\cdot\left(\cfrac{l}{d_1}\right)^3+0.007\cdot\left(\cfrac{l}{d_1}\right)^4

Loss coefficient

$$ζ=φ_0\cdot\left(1.43-1.3\cdotβ^2\right)\cdot\left(1-β^2\right)^2$$
$ζ=φ_0\cdot\left(1.43-1.3\cdotβ^2\right)\cdot\left(1-β^2\right)^2$
Equations in LaTeX code
ζ=φ_0\cdot\left(1.43-1.3\cdotβ^2\right)\cdot\left(1-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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