# The flow characteristic (crank mechanism)

## Values for calculation

$α$ $\mathrm{°}$
$β$ $\mathrm{°}$
$r$ $\mathrm{mm}$
$l$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$K_{Q-valve}[1]$
$K_{Q-valve}[2]$
$K_{Q-valve}[3]$
$K_{Q-valve}[4]$
$K_{Q-valve}[5]$
$K_{Q-valve}[6]$
$K_{Q-valve}[7]$
$K_{Q-valve}[8]$
$K_{Q-valve}[9]$
$K_{Q-valve}[10]$

## Calculation

### Stroke

$$S_{max}=\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}+r\cdot\cos{α}-\sqrt{l^2-\left(r\cdot\sin{\left(α+β\right)}-e\right)^2}-r\cdot\cos{\left(α+β\right)}$$
Stroke from open position
Angle rotation of the rocking motion
Stroke in the pivot position
Stroke percentage
Flow coefficient $K_{Q-valve}$
Flow coefficient
$s$ $β_S$ $S_S$ $S_{S\%}$ $K_{Q-valve}$ $K_Q$
$\mathrm{\%}$ $\mathrm{°}$ $\mathrm{mm}$ $\mathrm{\%}$ $\mathrm{ }$ $\mathrm{ }$
No data

$β_S \mathrm{[°]}$
 No data
$s\mathrm{[\%]}$

$$β_S=\cfrac{β}{100}\cdot s$$

$S_S \mathrm{[mm]}$
 No data
$s\mathrm{[\%]}$

$$S_S=S_{max}-\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}-r\cdot\cos{α}+\sqrt{l^2-\left(r\cdot\sin{\left(α+β-β_S\right)}-e\right)^2}+r\cdot\cos{\left(α+β-β_S\right)}$$

$S_{S\%} \mathrm{[\%]}$
 No data
$s\mathrm{[\%]}$

$$S_{S\%}=\cfrac{100}{S_{max}}\cdot S_S$$

$K_{Q-valve} \mathrm{[-]}$
 No data
$s\mathrm{[\%]}$

$K_Q \mathrm{[-]}$
 No data
$s\mathrm{[\%]}$

$\text{if }\ s= 0$
$$K_Q=K_{Q-valve}$$
$\text{else if }\ s= 100$
$$K_Q=K_{Q-valve}$$
$\text{else}$
$$K_Q=K_{Q-valve}-\cfrac{K_{Q-valve}-K_{Q-valve}[i+1]}{10}\cdot\left(S_{S\%}-s\right)$$