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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

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

Theoretical pressure in the valve at full opening

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

Pressure parameter

$$p=\cfrac{Δ_h}{H}$$

Effective closing time

$$t_{ef}=t\cdot c_{ef}$$

Volume elastic modulus

$$K=w^2\cdot ρ$$

Speed pressure waves in the pipe

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

Speed in the pipe

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

Water hammer

if $t_{ef} \geq \cfrac{2\cdot L}{a}$$$ΔP=\cfrac{L\cdot v_{max}}{t_{ef}\cdot g}$$else$$ΔP=\cfrac{a\cdot v_{max}}{g}$$

Requirements

$$0 < p \le 1$$