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Hydrodynamic calculation Howell-Bunger valve

Howell-Bunger valve D 90° 48° R 72° S 25° 40° a b c e f g +F x
Howell-Bunger valve

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} $
$ S $ $ \mathrm{mm} $
$ R $ $ \mathrm{mm} $
$ a $ $ \mathrm{mm} $
$ b $ $ \mathrm{mm} $
$ c $ $ \mathrm{mm} $
$ e $ $ \mathrm{mm} $
$ f $ $ \mathrm{mm} $
$ g $ $ \mathrm{mm} $
$ \{H\in\mathbb{R}\mid H>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.
$ H $ $ \mathrm{m} $
$ \{g\in\mathbb{R}\mid g>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.
$ g $ $ \mathrm{m/s^2} $
$ \{T\in\mathbb{R}\mid T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T $ $ \mathrm{°C} $
$ ρ $ $ \mathrm{kg/m^3} $
$ P_{SV} $ $ \mathrm{Pa} $
$ n $
$ \{ΔP\in\mathbb{R}\mid ΔP>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.
$ ΔP $ $ \mathrm{m} $
$ \{Σζ\in\mathbb{R}\mid Σζ>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.
$ Σζ $
$ \{h\in\mathbb{R}\mid h\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ h $ $ \mathrm{m} $
$ ρ_{air} $ $ \mathrm{kg/m^3} $
$ p_{air} $ $ \mathrm{Pa} $
$ \{h_j\in\mathbb{R}\mid h_j>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.
$ h_j $ $ \mathrm{m} $
Hydraulic jump behind the valve - model no.1 D 2.5 D L 1 L 2 h l h j
Hydraulic jump behind the valve - model no.1
Dimensional sketch - model no.1 x D 1.25 D 1 D 45° 2.5 D 2.5 D 30° 3 D 6 D 0.4D 2.76D 0.39D 0.86D 1.36D 1.39D 2.77 D 3.08 D 45° P u P u P 1 u-air P 2 u-air P 1 u-air P 2 u-air
Dimensional sketch - model no.1
Hydraulic jump behind the valve - model no.2 D 2.5 D L 1 L 2 h l h j
Hydraulic jump behind the valve - model no.2
Dimensional sketch - model no.2 D 2.82 D 3.33 D 45° 1.36D 3 D 6 D 30° 0.39D 2.56D 1.94D 0.39D 0.58D 45° 0.64D 2.5 D 1.11D 0.6D 0.44 D 0.1 D 4.36D 1.5 D 1.5 D P u P u P 1 u-air P 1 u-air P 2 u-air P 2 u-air
Dimensional sketch - model no.2
Hydraulic jump behind the valve - model no.3 h l h j D 1.2 D L 1 L 2
Hydraulic jump behind the valve - model no.3
Dimensional sketch - model no.3 D 1.82 D 2.33 D 45° 1.36D 3 D 6 D 30° 0.39D 2.56D 1.94D 45° 1.2 D 1.11D 0.6D 0.1 D 4.36D 1.5 D 1.5 D P u P u P 1 u-air P 1 u-air P 2 u-air P 2 u-air
Dimensional sketch - model no.3

Calculation

Flow

$$Q_{max}=\cfrac{1}{\sqrt{1+Σζ+\min\left(ζ\right)}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}$$
$Q_{max}=\cfrac{1}{\sqrt{1+Σζ+\min\left(ζ\right)}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}$
Equations in LaTeX code
Q_{max}=\cfrac{1}{\sqrt{1+Σζ+\min\left(ζ\right)}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}

Velocity in valve

$$v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}$$
$v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}$
Equations in LaTeX code
v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}

Theoretical pressure in the valve at full opening

$$Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left({\min\left(ζ\right)}+1\right)$$
$Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left({\min\left(ζ\right)}+1\right)$
Equations in LaTeX code
Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left({\min\left(ζ\right)}+1\right)

Pressure parameter

$$p=\cfrac{Δ_h}{H}$$
$p=\cfrac{Δ_h}{H}$
Equations in LaTeX code
p=\cfrac{Δ_h}{H}
$$0 < p \le 1$$
$0 < p \le 1$
Equations in LaTeX code
0 < p \le 1
Valve position
Flow coefficient
Coefficient of hydraulic force on body in the axis x
Loss coefficient
Reduced free flow area in the throttle control system
Relative flow
$ S/D $ $ K_Q $ $ K_{bx} $ $ ζ $ $ f_r $ $ Q_p $
$ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data