# Viscosity

Viscosity

Flowing is one of the characteristic properties of liquids. Some liquids flow more readily than others. Thus ether will move over a glass plate much more quickly than glycerol. The rate of flow depends on the nature of liquid and on the force which produces the flow. When a liquid flows between two plates or in a cylindrical tube, one layer slides fast another and a frictional force exists along the surface of contact between any two layers. This force opposes the relative motion between the two layers and is called viscous force.

If we consider any two thin layers, the lower (slower) layer exerts a viscous force on the upper, tending to drag it backward. Conversely, the upper (faster) layer exerts an equal viscous force on the layer but tending to drag forward. In other words, the viscous force tends to destroy the relative motion between the layers. Hence, if the flow of the liquid is to be maintained, some external force has to be applied. In the absence of any external force, the viscous force would soon bring the liquid to rest.

The property of a liquid owing to which it resists the relative motion of its parts is called viscosity”.

When the flow of the liquid becomes steady, there will be a constant difference in the velocity between two different layers (i. e. , velocity gradient). Newton deduced that the internal friction or viscosity would produce retarding force proportional to the velocity gradient (dV/ dx) (normal to the direction of flow) and to the area of contact (A) between the moving sheets of liquid.

I.e. $F \propto A.\dfrac{dV}{dx} \\ \text{or} F = \eta.A.\dfrac{dV}{dx}$

where $\eta$is constant and is known as Co-efficient of Viscosity.

Which may be defined as:

The tangential viscous or dragging force per unit area acting between layers of liquid in which unit velocity gradient is maintained in a direction normal to the layers”.

The co-efficient of viscosity, or simply known as viscosity has the dimension $ML^{-1}T$, and is measured in C.G.S. units i.e., poise (dyne per square centimeter). Common liquids range in viscosity from 0.002 poise (ether) to 8 poise (glycerol), that of water being about 0.01 poise. The reciprocal of the co-efficient of viscosity is called Fluidity.

Molecular viscosity may be defined as the product of viscosity and molecular surface i.e. ,

Molecular viscosity =Molecular surface X Viscosity

=$[\dfrac{M}{D}]^{-2/3} \times \eta$

It is constant for a given substance.

Fluidity,        $\phi = \dfrac{1}{\text{Viscosity} (\eta)}$

The determination of the absolute viscosity is not always convenient. But it is easier to compare the viscosity of two liquids and if the viscosity of one be known, that of the other is also determined. The Simple apparatus used for determining the relative flow is known as Ostwald’s Viscometer. The viscosity of given liquid may be calculated using the following formula:

$\dfrac{\eta_1}{\eta_2}$ $=\dfrac{t_1}{t_2} \times \dfrac{\rho _1}{\rho _2}$

Where,

$\eta_1$ = Viscosity of the given liquid

$\eta_2$ =Viscosity of water

$t_1$ =Time taken by a definite volume liquid to flow

$t_2$ =Time taken by the same volume water to flow

$p_1$ =Density of the given liquid

$p_2$ =Density of water

Example 1. Find out the viscosity of ethyl alcohol at $30^0C$ from the following data

(i)  Mean time of outflow for water = 60s.

(ii)  Mean time of outflow for ethyl alcohol 105s.

(iii)   Weight of empty pyknometer = 11.85 g

(iv)  Weight of pyknometer filled with water = 19.85 g.

(v)  Weight of pyknometer filled with alcohol =18.15 g.

(vi)  Viscosity af water at $30^0 C$ = 8.00 poise.

(vii)    Density of water 1 g/mL.

Solution: Apply the formula

$\dfrac{\eta_1}{\eta_2} = \dfrac{t_1}{t_2} \times \dfrac{\rho_1}{\rho_2}$

Given, $\eta_2 = 8, \eta_1 = ?, \\[3mm] t_1 = 105, \rho_2 = 1, t_2 = 60 \\[3mm] \rho_1 = \left(\dfrac{z- x}{y- x} \right) = \dfrac{18.15- 11.85}{19.85- 11.85} \\[3mm] \dfrac{6.30}{8.00} = 0.787$

Hence,

$\dfrac{\eta_1}{8} = \dfrac{105}{60} \times \dfrac{0.787}{1}$

Or

$\eta_1 = \dfrac{105}{60} \times 0.787 \times 11.025$

Therefore, the viscosity of ethyl alcohol at $30^0C$ = 11.025 poise.

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