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Flush mounted discharge from a conical diffuser

Flush mounted discharge from a conical diffuser d d E α
Flush mounted discharge from a conical diffuser

Values for calculation

$d$ $\mathrm{mm}$
$d_E$ $\mathrm{mm}$
$α$ $\mathrm{°}$
$f$

Calculation

Diameter ratio

$$β=\cfrac{d}{d_E}$$

Loss coefficient

$\text{if }\ α\le 20$
$$ζ=8.3\cdot\left[\tan{\left(α/2\right)}\right]^{1.75}\cdot\left(1-β^2\right)^2+\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}+β^4$$
$\text{else if }\ α\le 60\wedgeβ<0.5$
$$ζ=\left\{1.366\cdot\sin{\left[\cfrac{2\cdot π\cdot\left(α-15°\right)}{180}\right]}^{1/2}-0.17-3.28\cdot\left(0.0625-β^4\right)\cdot\sqrt{\cfrac{α-20°}{40°}}\right\}\cdot\left(1-β^2\right)^2+\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}+β^4$$
$\text{else if }\ α\le 60$
$$ζ=\left\{1.366\cdot\sin{\left[\cfrac{2\cdot π\cdot\left(α-15°\right)}{180}\right]}^{1/2}-0.17\right\}\cdot\left(1-β^2\right)^2+\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}+β^4$$
$\text{else if }\ α\le 180\wedgeβ<0.5$
$$ζ=\left[1.205-3.28\cdot\left(0.0625-β^4\right)-12.8\cdot β^6\cdot\sqrt{\cfrac{α-60°}{120°}}\right]\cdot\left(1-β^2\right)^2+β^4$$
$\text{else}$
$$ζ=\left(1.205-0.2\cdot\sqrt{\cfrac{α-60°}{120°}}\right)\cdot\left(1-β^2\right)^2+β^4$$

Discharge coefficient

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$