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Water hammer

Values for calculation

$ \{Q_{max}\in\mathbb{R}\mid Q_{max}>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.
$ Q_{max} $ $ \mathrm{m^3/s} $
$ \{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} $
$ \{D_p\in\mathbb{R}\mid D_p>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_p $ $ \mathrm{mm} $
$ \{L\in\mathbb{R}\mid L>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.
$ L $ $ \mathrm{m} $
$ \{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} $
$ w $ $ \mathrm{m\cdot\ s^{-1}} $
$ \{E\in\mathbb{R}\mid E>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.
$ E $ $ \mathrm{Pa} $
$ \{ζ\in\mathbb{R}\mid ζ>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.
$ ζ $
$ \{c_{ef}\in\mathbb{R}\mid c_{ef}>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.
$ c_{ef} $
$ \{t\in\mathbb{R}\mid t>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.
$ t $ $ \mathrm{s} $
$ \{e\in\mathbb{R}\mid e>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.
$ e $ $ \mathrm{mm} $

Calculation

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

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

Effective closing time

$$t_{ef}=t\cdot c_{ef}$$
$t_{ef}=t\cdot c_{ef}$
Equations in LaTeX code
t_{ef}=t\cdot c_{ef}

Volume elastic modulus

$$K=w^2\cdot ρ$$
$K=w^2\cdot ρ$
Equations in LaTeX code
K=w^2\cdot ρ

Speed pressure waves in the pipe

$$a=\cfrac{w}{\sqrt{1+\cfrac{D_p}{e}\cdot\cfrac{K}{E}}}$$
$a=\cfrac{w}{\sqrt{1+\cfrac{D_p}{e}\cdot\cfrac{K}{E}}}$
Equations in LaTeX code
a=\cfrac{w}{\sqrt{1+\cfrac{D_p}{e}\cdot\cfrac{K}{E}}}

Speed in the pipe

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

Water hammer

$\text{if }\ t_{ef}\geq \cfrac{2\cdot L}{a}$
$\text{if }\ t_{ef}\geq \cfrac{2\cdot L}{a}$
Equations in LaTeX code
\text{if }\ t_{ef}\geq \cfrac{2\cdot L}{a}
$$ΔP=\cfrac{L\cdot v_{max}}{t_{ef}\cdot g}$$
$ΔP=\cfrac{L\cdot v_{max}}{t_{ef}\cdot g}$
Equations in LaTeX code
ΔP=\cfrac{L\cdot v_{max}}{t_{ef}\cdot g}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ΔP=\cfrac{a\cdot v_{max}}{g}$$
$ΔP=\cfrac{a\cdot v_{max}}{g}$
Equations in LaTeX code
ΔP=\cfrac{a\cdot v_{max}}{g}
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