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When a fluid flows its movement can be characterized in one of the two types: steady or laminar and turbulent.
A fluid flow is laminar if each particle of the fluid follows a smooth path such that the paths of different particles never cross each other. And in the steady flow the velocity of the fluid at any point remains constant.
A fluid flow is turbulent after certain limit of speed so that the flow becomes irregular characterized by small whirls.
• To characterize the degree of internal friction of the fluid the term viscosity is used. Due to the viscosity, a part of the kinetic energy of the fluid is converted to internal energy.
• An ideal fluid can be considered to be non-viscous, incompressible with steady and ir-rotational flow.
• In the ir-rotational flow the fluid has no angular momentum about any point.
• The density is constant for an incompressible fluid.
• The velocity in a steady flow is constant at each point of the fluid.
• An object moving through a non-viscous fluid experiences zero viscosity.
Streamlines and Equation of Continuity:
The path taken by a fluid particle under steady flow is called a streamline. The velocity of the particle in the streamline is always tangent to the streamline. In such a motion the fluid particles cannot flow into or out of the tube of flow. If they do so, then the streamlines cross each other. Let us consider a non uniform pipe in which an ideal fluid is flowing as shown in the figure.
The particles in the fluid move along streamline in
steady flow. In the time t, the fluid at the bottom
end of the pipe moves a distance Δx1=v1t. If A1 is
the cross-sectional area in this region, then the mass
of the fluid contained in the left shaded region in the
figure is m1=ρA1Δx1=ρA1v1t, where ρ is the non-
changing density of the ideal fluid. Similarly, for the
fluid that moves at the upper end of the pipe in time
t has a mass m2=ρA2v2t. Since the mass is conserved,
we can write:
A1v1 = A2v2
= constant
This is called equation of continuity. It implies that the product of area and fluid speed at all points along the pipe is a constant for an incompressible fluid.
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