The motion of real fluids is very complicated and not yet fully understood. Instead , we shall discuss the motion of an ideal fluid, which is simpler to handle mathematically and yet provides useful results. Here are four assumptions that we make about our ideal fluid; they all are concerned with flow:
1. Steady flow In steady ( or laminar ) flow, we velocity of the moving fluid at any fixed point does not change with time. The gentle flow of water near the center of a quiet stream is steady ; the flow in a chain of rapids is not. Figure :
Shows a transition from steady flow to nonsteady ( or nonlaminar or turbulent ) flow for a rising stream of smoke. The speed of the smoke particles increases as they rise and, at a certain critical speed , the flow changes from steady to nonsteady.
2. Incompressible flow We assume , as for fluids at rest , thet our ideal fluid is incompressible ; that is, its density has a constant, uniform value.
3. Nonviscous flow Roughly speaking, the velocity of a fluid is a measure of how resistive the fluid is to flow . For example , thick honey is more resistive to flow than water, and so honey is said to be more viscous than water. Viscosity is the fluid analog of friction between solids; both are mechanismsby which the kinetic energy of moving objects can be transferred to thermal energy. In the absence of friction , a block could glide at constant speed along a horizontal surface. In the same way, an object moving through a nonviscous fluid would experience no viscous drag force – that is , no resistive force due to viscosity ; it could move at constant speed through the fluid. The british scientist Lord Rayleigh noted that in an ideal fluid a ship’s propeller would not work , but, on the other hand , in an ideal fluid a ship ( once set into motion ) would not need a propeller.
4. Irrotational flow Although I need not concern us further , we also assume that the flow is irrotational. To test for this property, let a tiny grain of dust move with the fluid. Although this test body may ( or may not ) move in a circular path, in irrotational flow the test body will not raotate about an axis through its own center of mass. For a loose analogy, the motion of Ferris wheel is rotational ; that of its passengers is irrotational.
We can make the flow of a flud visible bya adding a tracer. This might be a dye injected into many points across a liquid stream Figure :
Or smoke particles added to a gas flow. Each bit of a tracer follows is streamline , which is the path that a tiny element of the fluid would take as the fluid flows. The velocity of a particle is always tangent to the path taken by the particle . Here the particle is the fluid element, and its velocity v is always tangent to streamline figure :
For this reason , two streamlines can never intersect; if they did, than an element arriving at their intersection would have two different velocities simultaneously – an impossibility.
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