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Water hammer

Values for calculation

$Q_{max}$ $\mathrm{m^3/s}$
$D$ $\mathrm{mm}$
$D_p$ $\mathrm{mm}$
$L$ $\mathrm{m}$
$H$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$w$ $\mathrm{m/s}$
$E$ $\mathrm{Pa}$
$ζ$
$c_{ef}$
$t$ $\mathrm{s}$
$e$ $\mathrm{mm}$

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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