Formula: Fluid Between Two Parallel Plates Viscosity Velocity Inner surface Force Distance
$$\eta ~=~ \frac{F \, d}{ v_0 \, A }$$
$$\eta ~=~ \frac{F \, d}{ v_0 \, A }$$
$$v_0 ~=~ \frac{F \, d}{ \eta \, A }$$
$$A ~=~ \frac{F \, d}{ \eta \, v_0 }$$
$$F ~=~ \frac{A \, \eta \, v_0}{ d }$$
$$d ~=~ \frac{A \, \eta \, v_0}{ F }$$
Viscosity
$$ \eta $$ Unit $$ \frac{\mathrm{kg} \cdot \mathrm{m}}{ \mathrm s } $$
The greater the viscosity of a liquid, the more viscous the liquid. The liquid is located (for the use of this formula) between two plates parallel to each other.
| Liquid | Viscosity \( \eta \) |
|---|---|
| Olive oil | \( 108 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Honey | \( 10\,000 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Glycerin | \( 1500 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Water | \( 1.008 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Tar | \( 100\,000 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
Velocity
$$ v_0 $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
One of the plates between which the liquid is located is displaced in parallel. The liquid directly at the shifting plate has a maximum velocity \(v_0\).
Inner surface
$$ A $$ Unit $$ \mathrm{m}^2 $$
The surface of one side of the plate.
Force
$$ \boldsymbol{F} $$ Unit $$ \mathrm{N} = \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{s}^2} $$
A force \(F\) is applied parallel to a plate, resulting in a shear stress \(F/A\) on the liquid.
Distance
$$ d $$ Unit $$ \mathrm{m} $$
Distance between the two plates.