# Poisuille is sI unit of viscosity ? And one pois e is equal to ?

Nov 16, 2017

see below

#### Explanation:

Poise is the unity of measure of dynamic viscosity in cgs sistem. $1 p o i s e = 1 \frac{g}{c m \times s}$. Viscosity of water at room temperature is 0.01 P = 1 cP
In SI the unity of measure of dynamic viscosity is $\frac{K g}{m \times s} = 10 P$

Nov 16, 2017

$\left[\setminus \mu\right] = \setminus \frac{\left[F\right]}{\left[A\right] \left[\setminus \frac{\setminus \partial u}{\setminus \partial y}\right]}$
$1$ poise  = ("dyne")/(cm^2.s^{-1}) = "dyne".s.cm^{-2}=g.cm^{-1}.s^{-1}

#### Explanation:

Dynamic Viscosity: Dynamic viscosity of a fluid is its resistance to shearing forces. Consider a layer of fluid between two horizontal plates, with the bottom plate held fixed. If we want to move the top plate at a constant velocity we must apply a shear force that equilibrates with the viscous drag force.

This shear force is proportional to the cross sectional area and the velocity gradient.

F \propto A \frac{\delu}{\dely}; \qquad F = \muA\frac{\delu}{\dely}.

$\setminus \mu$ is the coefficient of dynamic viscosity. Its cgs unit is poisuille or simply poise.

$\left[\setminus \frac{\setminus \partial u}{\setminus \partial y}\right] = \frac{c m . {s}^{- 1}}{c m} = {s}^{- 1}$
$\left[\setminus \mu\right] = \setminus \frac{\left[F\right]}{\left[A\right] \left[\setminus \frac{\setminus \partial u}{\setminus \partial y}\right]}$
$1$ poise  = ("dyne")/(cm^2.s^{-1}) = "dyne".s.cm^{-2} = g.cm^{-1}.s^{-1}
$1$ dyne $= g . c m . {s}^{- 2}$

What is velocity gradient?:The fluid can be seen as made of infinite number of infinitesimal layers. The layer touching the top plate will be moving with the velocity of the plate while the layer touching the bottom plate will be at rest. All other layers will be moving parallel to each other, at velocities between these two extreme values with a unique velocity gradient, $\setminus \frac{\setminus \partial u}{\setminus \partial y}$. If the flow is laminar this velocity gradient is linear.