Hydrodynamic calculation Howell-Bunger valve

Hydraulic engineering
Valves
Hydrodynamic calculation Howell-Bunger valve

Howell-Bunger valve

Values for calculation

Model number for Howell-Bunger valve

Valve diameter

$ \{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} $

Dimension $ S $

$$S=0.6\cdot D$$

$S=0.6\cdot D$

Equations in LaTeX code

S=0.6\cdot D

$ S $ $ \mathrm{mm} $

Dimension $ R $

$$R=0.5555\cdot D$$

$R=0.5555\cdot D$

Equations in LaTeX code

R=0.5555\cdot D

$ R $ $ \mathrm{mm} $

Dimension $ a $

$$a=0.1583\cdot D$$

$a=0.1583\cdot D$

Equations in LaTeX code

a=0.1583\cdot D

$ a $ $ \mathrm{mm} $

Dimension $ b $

$$b=0.1361\cdot D$$

$b=0.1361\cdot D$

Equations in LaTeX code

b=0.1361\cdot D

$ b $ $ \mathrm{mm} $

Dimension $ c $

$$c=0.5694\cdot D$$

$c=0.5694\cdot D$

Equations in LaTeX code

c=0.5694\cdot D

$ c $ $ \mathrm{mm} $

Dimension $ e $

$$e=0.6861\cdot D$$

$e=0.6861\cdot D$

Equations in LaTeX code

e=0.6861\cdot D

$ e $ $ \mathrm{mm} $

Dimension $ f $

$$f=0.1222\cdot D$$

$f=0.1222\cdot D$

Equations in LaTeX code

f=0.1222\cdot D

$ f $ $ \mathrm{mm} $

Dimension $ g $

$$g=0.0666\cdot D$$

$g=0.0666\cdot D$

Equations in LaTeX code

g=0.0666\cdot D

$ g $ $ \mathrm{mm} $

Static head

$ \{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.

Static head

$$H\le 8000$$

$H\le 8000$

Equations in LaTeX code

H\le 8000

$ H $ $ \mathrm{m} $

Gravitational acceleration

$ \{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} $

The water temperature

$ \{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.

The water temperature

$$T\le 2000$$

$T\le 2000$

Equations in LaTeX code

T\le 2000

$ T $ $ \mathrm{°C} $

Density

$$ρ=ρ$$

$ρ=ρ$

Equations in LaTeX code

ρ=ρ

$ ρ $ $ \mathrm{kg/m^3} $

Saturated vapor pressure

$\text{if }\ \left(T+273.15\right)\le 623.15$

Equations in LaTeX code

\text{if }\ \left(T+273.15\right)\le 623.15

$$P_{SV}=1\cdot10^6\cdot\left(\cfrac{2\cdot C}{-B+\sqrt{B^2-4\cdot A\cdot C}}\right)^4$$

$P_{SV}=1\cdot10^6\cdot\left(\cfrac{2\cdot C}{-B+\sqrt{B^2-4\cdot A\cdot C}}\right)^4$

Equations in LaTeX code

P_{SV}=1\cdot10^6\cdot\left(\cfrac{2\cdot C}{-B+\sqrt{B^2-4\cdot A\cdot C}}\right)^4

$\text{else}$

Equations in LaTeX code

\text{else}

$$P_{SV}=1\cdot10^6\cdot (0.34805185628969\cdot10^3+\left(-0.11671859879975\cdot10^1\cdot \left(T+273.15\right)\right)+0.10192970039326\cdot10^{-2}\cdot \left(T+273.15\right)^2)$$

$P_{SV}=1\cdot10^6\cdot (0.34805185628969\cdot10^3+\left(-0.11671859879975\cdot10^1\cdot \left(T+273.15\right)\right)+0.10192970039326\cdot10^{-2}\cdot \left(T+273.15\right)^2)$

Equations in LaTeX code

P_{SV}=1\cdot10^6\cdot (0.34805185628969\cdot10^3+\left(-0.11671859879975\cdot10^1\cdot \left(T+273.15\right)\right)+0.10192970039326\cdot10^{-2}\cdot \left(T+273.15\right)^2)

$ P_{SV} $ $ \mathrm{Pa} $

Aeration

$ n $

yes

Water hammer

$ \{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} $

Loss before valve

$ \{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 $

Height above sea level

$ \{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.

Height above sea level

$$h+H\le 8000$$

$h+H\le 8000$

Equations in LaTeX code

h+H\le 8000

$ h $ $ \mathrm{m} $

Density air

$$ρ_{air}=\cfrac{p_{air}}{R\cdot T}$$

$ρ_{air}=\cfrac{p_{air}}{R\cdot T}$

Equations in LaTeX code

ρ_{air}=\cfrac{p_{air}}{R\cdot T}

$ ρ_{air} $ $ \mathrm{kg/m^3} $

Atmospheric pressure air

$\text{if }\ β=0$

Equations in LaTeX code

\text{if }\ β=0

$$p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]$$

$p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]$

Equations in LaTeX code

p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]

$\text{else}$

Equations in LaTeX code

\text{else}

$$p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}$$

$p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}$

Equations in LaTeX code

p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}

$ p_{air} $ $ \mathrm{Pa} $

Water depth behind the hydraulic jump

$ \{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

Dimensional sketch - model no.1

Hydraulic jump behind the valve - model no.2

Dimensional sketch - model no.2

Hydraulic jump behind the valve - model no.3

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

Valve position

$$S/D=\left\{0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0\right\}$$

$S/D=\left\{0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0\right\}$

Equations in LaTeX code

S/D=\left\{0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0\right\}

Flow coefficient

$\text{if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 3.6$

Equations in LaTeX code

\text{if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 3.6

$$K_Q=\left\{0.798, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}$$

$K_Q=\left\{0.798, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.798, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 4.5

$$K_Q=\left\{0.818, 0.807, 0.782, 0.746, 0.700, 0.638, 0.570, 0.493, 0.408, 0.316, 0.221, 0.112, 1E-100\right\}$$

$K_Q=\left\{0.818, 0.807, 0.782, 0.746, 0.700, 0.638, 0.570, 0.493, 0.408, 0.316, 0.221, 0.112, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.818, 0.807, 0.782, 0.746, 0.700, 0.638, 0.570, 0.493, 0.408, 0.316, 0.221, 0.112, 1E-100\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5

$$K_Q=\left\{0.875, 0.856, 0.823, 0.778, 0.722, 0.654, 0.577, 0.496, 0.408, 0.316, 0.221, 0.112, 1E-100\right\}$$

$K_Q=\left\{0.875, 0.856, 0.823, 0.778, 0.722, 0.654, 0.577, 0.496, 0.408, 0.316, 0.221, 0.112, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.875, 0.856, 0.823, 0.778, 0.722, 0.654, 0.577, 0.496, 0.408, 0.316, 0.221, 0.112, 1E-100\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 3.6$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 3.6

$$K_Q=\left\{0.822, 0.808, 0.779, 0.737, 0.686, 0.625, 0.551, 0.473, 0.388, 0.296, 0.194, 0.062, 1E-100\right\}$$

$K_Q=\left\{0.822, 0.808, 0.779, 0.737, 0.686, 0.625, 0.551, 0.473, 0.388, 0.296, 0.194, 0.062, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.822, 0.808, 0.779, 0.737, 0.686, 0.625, 0.551, 0.473, 0.388, 0.296, 0.194, 0.062, 1E-100\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}\geq 3.6$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}\geq 3.6

$$K_Q=\left\{0.833, 0.820, 0.793, 0.750, 0.703, 0.642, 0.568, 0.489, 0.404, 0.312, 0.209, 0.077, 1E-100\right\}$$

$K_Q=\left\{0.833, 0.820, 0.793, 0.750, 0.703, 0.642, 0.568, 0.489, 0.404, 0.312, 0.209, 0.077, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.833, 0.820, 0.793, 0.750, 0.703, 0.642, 0.568, 0.489, 0.404, 0.312, 0.209, 0.077, 1E-100\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 3$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 3

$$K_Q=\left\{0.834, 0.817, 0.788, 0.746, 0.688, 0.624, 0.546, 0.463, 0.374, 0.281, 0.182, 0.075, 1E-100\right\}$$

$K_Q=\left\{0.834, 0.817, 0.788, 0.746, 0.688, 0.624, 0.546, 0.463, 0.374, 0.281, 0.182, 0.075, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.834, 0.817, 0.788, 0.746, 0.688, 0.624, 0.546, 0.463, 0.374, 0.281, 0.182, 0.075, 1E-100\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}\geq 3$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}\geq 3

$$K_Q=\left\{0.854, 0.840, 0.810, 0.769, 0.714, 0.647, 0.569, 0.487, 0.395, 0.303, 0.200, 0.094, 1E-100\right\}$$

$K_Q=\left\{0.854, 0.840, 0.810, 0.769, 0.714, 0.647, 0.569, 0.487, 0.395, 0.303, 0.200, 0.094, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.854, 0.840, 0.810, 0.769, 0.714, 0.647, 0.569, 0.487, 0.395, 0.303, 0.200, 0.094, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 2.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 2.5

$$K_Q=\left\{0.798, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}$$

$K_Q=\left\{0.798, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.798, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 3.6$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 3.6

$$K_Q=\left\{0.796, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}$$

$K_Q=\left\{0.796, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.796, 0.789, 0.766, 0.731, 0.682, 0.621, 0.550, 0.474, 0.390, 0.300, 0.210, 0.112, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 4.5

$$K_Q=\left\{0.769, 0.762, 0.744, 0.739, 0.720, 0.629, 0.538, 0.468, 0.392, 0.307, 0.217, 0.111, 1E-100\right\}$$

$K_Q=\left\{0.769, 0.762, 0.744, 0.739, 0.720, 0.629, 0.538, 0.468, 0.392, 0.307, 0.217, 0.111, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.769, 0.762, 0.744, 0.739, 0.720, 0.629, 0.538, 0.468, 0.392, 0.307, 0.217, 0.111, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5

$$K_Q=\left\{0.874, 0.854, 0.820, 0.775, 0.719, 0.651, 0.575, 0.494, 0.407, 0.315, 0.221, 0.112, 1E-100\right\}$$

$K_Q=\left\{0.874, 0.854, 0.820, 0.775, 0.719, 0.651, 0.575, 0.494, 0.407, 0.315, 0.221, 0.112, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.874, 0.854, 0.820, 0.775, 0.719, 0.651, 0.575, 0.494, 0.407, 0.315, 0.221, 0.112, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 2.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 2.5

$$K_Q=\left\{0.816, 0.804, 0.778, 0.734, 0.681, 0.621, 0.548, 0.472, 0.388, 0.296, 0.194, 0.062, 1E-100\right\}$$

$K_Q=\left\{0.816, 0.804, 0.778, 0.734, 0.681, 0.621, 0.548, 0.472, 0.388, 0.296, 0.194, 0.062, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.816, 0.804, 0.778, 0.734, 0.681, 0.621, 0.548, 0.472, 0.388, 0.296, 0.194, 0.062, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 3.6$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 3.6

$$K_Q=\left\{0.820, 0.808, 0.781, 0.738, 0.686, 0.623, 0.548, 0.470, 0.385, 0.294, 0.193, 0.062, 1E-100\right\}$$

$K_Q=\left\{0.820, 0.808, 0.781, 0.738, 0.686, 0.623, 0.548, 0.470, 0.385, 0.294, 0.193, 0.062, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.820, 0.808, 0.781, 0.738, 0.686, 0.623, 0.548, 0.470, 0.385, 0.294, 0.193, 0.062, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 4.5

$$K_Q=\left\{0.831, 0.815, 0.786, 0.747, 0.703, 0.640, 0.564, 0.487, 0.403, 0.311, 0.208, 0.077, 1E-100\right\}$$

$K_Q=\left\{0.831, 0.815, 0.786, 0.747, 0.703, 0.640, 0.564, 0.487, 0.403, 0.311, 0.208, 0.077, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.831, 0.815, 0.786, 0.747, 0.703, 0.640, 0.564, 0.487, 0.403, 0.311, 0.208, 0.077, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5

$$K_Q=\left\{0.830, 0.817, 0.789, 0.747, 0.700, 0.640, 0.566, 0.488, 0.403, 0.311, 0.208, 0.077, 1E-100\right\}$$

$K_Q=\left\{0.830, 0.817, 0.789, 0.747, 0.700, 0.640, 0.566, 0.488, 0.403, 0.311, 0.208, 0.077, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.830, 0.817, 0.789, 0.747, 0.700, 0.640, 0.566, 0.488, 0.403, 0.311, 0.208, 0.077, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 2$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 2

$$K_Q=\left\{0.821, 0.808, 0.782, 0.740, 0.682, 0.619, 0.542, 0.462, 0.376, 0.282, 0.183, 0.075, 1E-100\right\}$$

$K_Q=\left\{0.821, 0.808, 0.782, 0.740, 0.682, 0.619, 0.542, 0.462, 0.376, 0.282, 0.183, 0.075, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.821, 0.808, 0.782, 0.740, 0.682, 0.619, 0.542, 0.462, 0.376, 0.282, 0.183, 0.075, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 3$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 3

$$K_Q=\left\{0.812, 0.802, 0.780, 0.723, 0.652, 0.587, 0.511, 0.448, 0.374, 0.281, 0.182, 0.075, 1E-100\right\}$$

$K_Q=\left\{0.812, 0.802, 0.780, 0.723, 0.652, 0.587, 0.511, 0.448, 0.374, 0.281, 0.182, 0.075, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.812, 0.802, 0.780, 0.723, 0.652, 0.587, 0.511, 0.448, 0.374, 0.281, 0.182, 0.075, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 4$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 4

$$K_Q=\left\{0.840, 0.830, 0.804, 0.758, 0.699, 0.623, 0.554, 0.478, 0.391, 0.300, 0.198, 0.093, 1E-100\right\}$$

$K_Q=\left\{0.840, 0.830, 0.804, 0.758, 0.699, 0.623, 0.554, 0.478, 0.391, 0.300, 0.198, 0.093, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.840, 0.830, 0.804, 0.758, 0.699, 0.623, 0.554, 0.478, 0.391, 0.300, 0.198, 0.093, 1E-100\right\}

$\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}\geq 4$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{yes}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}\geq 4

$$K_Q=\left\{0.864, 0.846, 0.812, 0.771, 0.715, 0.651, 0.565, 0.482, 0.389, 0.298, 0.197, 0.093, 1E-100\right\}$$

$K_Q=\left\{0.864, 0.846, 0.812, 0.771, 0.715, 0.651, 0.565, 0.482, 0.389, 0.298, 0.197, 0.093, 1E-100\right\}$

Equations in LaTeX code

K_Q=\left\{0.864, 0.846, 0.812, 0.771, 0.715, 0.651, 0.565, 0.482, 0.389, 0.298, 0.197, 0.093, 1E-100\right\}

$\text{else}$

Equations in LaTeX code

\text{else}

$$K_Q=\left\{\right\}$$

$K_Q=\left\{\right\}$

Equations in LaTeX code

K_Q=\left\{\right\}

Coefficient of hydraulic force on body in the axis x

$\text{if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 1.2$

Equations in LaTeX code

\text{if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 1.2

$$K_{bx}=\left\{0.374, 0.385, 0.400, 0.416, 0.440, 0.468, 0.512, 0.574, 0.663, 0.781, 0.933, 1.104, 1\right\}$$

$K_{bx}=\left\{0.374, 0.385, 0.400, 0.416, 0.440, 0.468, 0.512, 0.574, 0.663, 0.781, 0.933, 1.104, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.374, 0.385, 0.400, 0.416, 0.440, 0.468, 0.512, 0.574, 0.663, 0.781, 0.933, 1.104, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 2.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 2.5

$$K_{bx}=\left\{0.330, 0.341, 0.356, 0.377, 0.403, 0.438, 0.490, 0.560, 0.657, 0.784, 0.947, 1.050, 1\right\}$$

$K_{bx}=\left\{0.330, 0.341, 0.356, 0.377, 0.403, 0.438, 0.490, 0.560, 0.657, 0.784, 0.947, 1.050, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.330, 0.341, 0.356, 0.377, 0.403, 0.438, 0.490, 0.560, 0.657, 0.784, 0.947, 1.050, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 3.6$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 3.6

$$K_{bx}=\left\{0.186, 0.200, 0.225, 0.254, 0.292, 0.349, 0.428, 0.518, 0.638, 0.774, 0.920, 1.036, 1\right\}$$

$K_{bx}=\left\{0.186, 0.200, 0.225, 0.254, 0.292, 0.349, 0.428, 0.518, 0.638, 0.774, 0.920, 1.036, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.186, 0.200, 0.225, 0.254, 0.292, 0.349, 0.428, 0.518, 0.638, 0.774, 0.920, 1.036, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}< 4.5

$$K_{bx}=\left\{0.355, 0.361, 0.369, 0.382, 0.402, 0.428, 0.469, 0.523, 0.602, 0.700, 0.831, 0.992, 1\right\}$$

$K_{bx}=\left\{0.355, 0.361, 0.369, 0.382, 0.402, 0.428, 0.469, 0.523, 0.602, 0.700, 0.831, 0.992, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.355, 0.361, 0.369, 0.382, 0.402, 0.428, 0.469, 0.523, 0.602, 0.700, 0.831, 0.992, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 1\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5

$$K_{bx}=\left\{0.340, 0.362, 0.386, 0.413, 0.442, 0.478, 0.524, 0.572, 0.629, 0.700, 0.804, 0.972, 1\right\}$$

$K_{bx}=\left\{0.340, 0.362, 0.386, 0.413, 0.442, 0.478, 0.524, 0.572, 0.629, 0.700, 0.804, 0.972, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.340, 0.362, 0.386, 0.413, 0.442, 0.478, 0.524, 0.572, 0.629, 0.700, 0.804, 0.972, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 1.2$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 1.2

$$K_{bx}=\left\{0.276, 0.296, 0.321, 0.352, 0.396, 0.450, 0.511, 0.588, 0.691, 0.814, 0.945, 1.035, 1\right\}$$

$K_{bx}=\left\{0.276, 0.296, 0.321, 0.352, 0.396, 0.450, 0.511, 0.588, 0.691, 0.814, 0.945, 1.035, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.276, 0.296, 0.321, 0.352, 0.396, 0.450, 0.511, 0.588, 0.691, 0.814, 0.945, 1.035, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 2.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 2.5

$$K_{bx}=\left\{0.357, 0.380, 0.405, 0.432, 0.463, 0.502, 0.554, 0.624, 0.716, 0.827, 0.957, 1.042, 1\right\}$$

$K_{bx}=\left\{0.357, 0.380, 0.405, 0.432, 0.463, 0.502, 0.554, 0.624, 0.716, 0.827, 0.957, 1.042, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.357, 0.380, 0.405, 0.432, 0.463, 0.502, 0.554, 0.624, 0.716, 0.827, 0.957, 1.042, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 3.6$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 3.6

$$K_{bx}=\left\{0.375, 0.358, 0.360, 0.377, 0.406, 0.442, 0.490, 0.548, 0.634, 0.750, 0.909, 1.063, 1\right\}$$

$K_{bx}=\left\{0.375, 0.358, 0.360, 0.377, 0.406, 0.442, 0.490, 0.548, 0.634, 0.750, 0.909, 1.063, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.375, 0.358, 0.360, 0.377, 0.406, 0.442, 0.490, 0.548, 0.634, 0.750, 0.909, 1.063, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}< 4.5

$$K_{bx}=\left\{0.306, 0.330, 0.356, 0.384, 0.416, 0.455, 0.502, 0.564, 0.650, 0.765, 0.907, 1.020, 1\right\}$$

$K_{bx}=\left\{0.306, 0.330, 0.356, 0.384, 0.416, 0.455, 0.502, 0.564, 0.650, 0.765, 0.907, 1.020, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.306, 0.330, 0.356, 0.384, 0.416, 0.455, 0.502, 0.564, 0.650, 0.765, 0.907, 1.020, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 2\wedge\cfrac{h_j}{D\cdot 1000}\geq 4.5

$$K_{bx}=\left\{0.268, 0.287, 0.310, 0.334, 0.362, 0.398, 0.446, 0.511, 0.596, 0.702, 0.848, 1.069, 1\right\}$$

$K_{bx}=\left\{0.268, 0.287, 0.310, 0.334, 0.362, 0.398, 0.446, 0.511, 0.596, 0.702, 0.848, 1.069, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.268, 0.287, 0.310, 0.334, 0.362, 0.398, 0.446, 0.511, 0.596, 0.702, 0.848, 1.069, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 1$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 1

$$K_{bx}=\left\{0.320, 0.342, 0.380, 0.428, 0.483, 0.550, 0.621, 0.695, 0.775, 0.861, 0.952, 1.033, 1\right\}$$

$K_{bx}=\left\{0.320, 0.342, 0.380, 0.428, 0.483, 0.550, 0.621, 0.695, 0.775, 0.861, 0.952, 1.033, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.320, 0.342, 0.380, 0.428, 0.483, 0.550, 0.621, 0.695, 0.775, 0.861, 0.952, 1.033, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 2$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 2

$$K_{bx}=\left\{0.353, 0.375, 0.407, 0.446, 0.491, 0.543, 0.599, 0.659, 0.728, 0.822, 0.939, 1.048, 1\right\}$$

$K_{bx}=\left\{0.353, 0.375, 0.407, 0.446, 0.491, 0.543, 0.599, 0.659, 0.728, 0.822, 0.939, 1.048, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.353, 0.375, 0.407, 0.446, 0.491, 0.543, 0.599, 0.659, 0.728, 0.822, 0.939, 1.048, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 3$

Equations in LaTeX code

\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 3

$$K_{bx}=\left\{0.350, 0.350, 0.357, 0.375, 0.405, 0.450, 0.519, 0.598, 0.689, 0.793, 0.904, 0.996, 1\right\}$$

$K_{bx}=\left\{0.350, 0.350, 0.357, 0.375, 0.405, 0.450, 0.519, 0.598, 0.689, 0.793, 0.904, 0.996, 1\right\}$

Equations in LaTeX code

K_{bx}=\left\{0.350, 0.350, 0.357, 0.375, 0.405, 0.450, 0.519, 0.598, 0.689, 0.793, 0.904, 0.996, 1\right\}

$\text{else if }\ \text{n}= \text{no}\wedge \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3\wedge\cfrac{h_j}{D\cdot 1000}< 4$

Menu

Hydrodynamic calculation Howell-Bunger valve

Values for calculation

Calculation

Flow

Velocity in valve

Theoretical pressure in the valve at full opening

Pressure parameter