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Round-edged orifice in a straight pipe

Round-edged orifice in a straight pipe d d o r
Round-edged orifice in a straight pipe

Values for calculation

$d$ $\mathrm{mm}$
$d_o$ $\mathrm{mm}$
$r$ $\mathrm{mm}$

Calculation

Diameter ratio

$$β=\cfrac{d_o}{d}$$

Jet contraction ratio

$$λ=1+0.622\cdot\left(1-0.3\cdot\sqrt{\cfrac{r}{d_o}}-0.7\cdot\sqrt{\cfrac{r}{d_o}}\right)^4\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$$

Loss coefficient

$$ζ=0.0696\cdot\left(1-0.569\cdot\cfrac{r}{d_o}\right)\cdot\left(1-\sqrt{\cfrac{r}{d_o}}\cdot β\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2$$

Discharge coefficient

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$