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Which of the following is not a property of an Ideal fluid.
1. It is incompressible
2. It has viscosity
3. It has no viscosity
4. Flow is Irrotational

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Correct Answer - Option 2 : It has viscosity

Explanation:

Ideal Fluid: An ideal fluid is a fluid that is incompressible and no internal resistance to flow, i.e. zero viscosity. In addition, ideal fluid particles undergo no rotation about their center-of-mass i.e. irrotational. An ideal fluid can flow in a circular pattern, but the individual fluid particles are irrotational. They don't exist.

Real Fluids: They have viscosity and are compressible, and fluid particle can rotate about their center of mass. Real fluids exhibit all of the properties of ideal fluid to some degree, but we shall often model fluids as ideal in order to approximate the behavior of real fluids.

Viscosity: The viscosity of a fluid is a measure of its resistance to deformation at a given rate. Denoted by μ.

\(\tau = μ \frac {du}{dy}\)

Here μ = Coefficient of dynamic viscosity; \(\frac {du}{dy}\) = Velocity gradient;

Kinematic Viscosity: It is a measure of a fluid's internal resistance to flow under gravitational forces. It is determined by measuring the time in seconds, required for a fixed volume of fluid to flow a known distance by gravity through a capillary within a calibrated viscometer at a closely controlled temperature. Denoted by ν.

\(\nu = \frac {\mu }{\rho}\)

Compressibility: If compression and expansion have a significant effect on the fluid density, the fluid is called a compressible fluid. Mathematically,

\(β = -\frac {1}{V}\frac {\partial V }{\partial p}\)

Here β = Compressibility factor; V = Volume of fluid; p = Applied pressure;

If β = 0, it means fluid is incompressible.

Irrotational Flow: It is a flow in which each element of the moving fluid undergoes no net rotation with respect to a chosen coordinate axes from one instant to other. Curl of the fluid velocity is zero.

\(\nabla \times \vec {v} =0\)

Rotational Flow: Flow of a fluid in which the curl of the fluid velocity is not zero, so that each minute particle of fluid rotates about its own axis. Also known as rotational motion.

\(\nabla \times \vec {v} \ne0\)

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