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Bevel-edged orifice in a straight pipe

Bevel-edged orifice in a straight pipe d d o ψ l
Bevel-edged orifice in a straight pipe

Values for calculation

$d$ $\mathrm{mm}$
$d_o$ $\mathrm{mm}$
$ψ$ $\mathrm{°}$
$l$ $\mathrm{mm}$

Calculation

Diameter ratio

$$β=\cfrac{d_o}{d}$$

$$β\le\cfrac{1}{1+2\cdot\cfrac{l}{d_o}\cdot\tan{ψ}}$$

Coefficient $ C_b $

$$C_b=\left(1-\cfrac{ψ}{90}\right)\cdot\left(\cfrac{ψ}{90}\right)^{\cfrac{1}{2+l/d_o}}$$

Jet contraction ratio

$$λ=1+0.622\cdot\left[1-C_b\cdot\left(\cfrac{l}{d_o}\right)^{\cfrac{1-\sqrt[4]{l/d_o}}{2}}\right]\cdot\left(1-0.215\cdot β^2-0.785\cdot β^5\right)$$

Loss coefficient

$$ζ=0.0696\cdot\left(1-C_b\cdot\cfrac{l}{d_o}\right)\cdot\left(1+0.42\cdot\sqrt{\cfrac{l}{d_o}}\cdot β^2\right)\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-β^2\right)^2$$

Discharge coefficient

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$