**Viscous Forces**- These are forces which has tendency to oppose relative motion between different layers of liquid or gases.

**Viscosity**– Viscosity is the characteristic of a liquid due to which it opposes the relative motion between its various layers.

• Viscosity is applicable to both liquid and gases.

• The viscosity of a liquid is because of cohesive forces between layers.

• Viscosity is liquid is less than viscosity of gases.

• Solid has no viscosity.

• Viscosity of an ideal fluid is zero.

• Viscosity of liquids decreases with rise in temperature.

• Viscosity of gases decreases with rise in temperature.

• Viscosity of fluids is measured in terms of “coefficient of Viscosity”.

• The SI Unit of viscosity is decapoise expressed in kg/ms or Pascal Second i.e. Pa-s.

• The viscosity is generally is generally denoted by Greek Symbol η.

**Viscosity of some substances**

• Viscosity of air (20oC): - 1.83x10-5 Pa-s

• Viscosity of water (20oC): 1.0x10-3 Pa-s

• Viscosity of honey (20oC): 1000 Pa-s

__• In liquids viscosity is due to the cohesive forces between the molecules and in gases the viscosity is due to collisions between the molecules.__

**Points to remember**

• The work done by viscous forces converts ordered energy into thermal energy.

• For a fluid flowing in a long horizontal pipe, the pressure drops along the pipe in the direction of the flow. The faster the fluid is flowing, the larger is the pressure drop.

• If the viscosity η is a constant, independent of flow speed, then the fluid is termed a Newtonian fluid.

• When η does depend on the velocity of flow, then the fluid is called non-Newtonian or complex.

• Blood is a mixture of a Newtonian and a non-Newtonian fluid. It contains corpuscles and other suspended particles.

• A corn starch - water mixture is another example of a non-Newtonian fluid.

**Terminal Velocity**- The terminal velocity of a falling body occurs during free fall when a falling body experiences zero acceleration. This is because of the retarding force known as air resistance. Air resistance exists because air molecules collide into a falling body creating an upward force opposite gravity. This upward force will eventually balance the falling body's weight. It will continue to fall at constant velocity known as the terminal velocity.

**Streamline Flow**- The streamline flow is the flow of a gas or liquid in which the velocity at any point is relatively steady.

**Laminar flow**– The laminar flow is the nonturbulent streamline flow in parallel layers.

Critical Velocity - Critical velocity is the velocity of a liquid flow upto which its flow is streamlined and after which its flow becomes turbulent. The critical velocity depends on coefficient of viscosity 'h', density of the liquid 'r', and radius of the tube (r). Mathematically, Critically Velocity,

where k is constant of proportionality

### Daniel Bernoulli's Principle Theorem

Bernoulli's theorem explores the behaviour of the ideal fluid flowing through the pipe. This important principle in fluid mechanics is found by Daniel Bernoulli in 1738.

The statement of Bernoulli’s Theorem- Bernoulli's theorem states that when a liquid is flowing, the total of the pressure energy, kinetic energy and potential energy per unit mass should be constant.

**Venturimeter is a device used to measure rate of flow of liquid, which works on Bernoulli’s Theorem.**

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