Ideal fluids in Motion

Ideal fluids in Motion

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 few:

1. Steady flow In steady (or laminar) flow, the velocity of the moving fluid at any fixed point does not change with time, either in magnitude or in direction. The gentle flow of water near the center of a quiet stream is steady: that in a chain of
rapids is not. Figure IS-II shows a transit  ion from steady flow to instead (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 unsteady (that is. from laminar to nonlaminar flow).

2, Incompressible flow We assume, as we have already done for fluids at rest, that our ideal fluid is incompressible: that is, its density has a constant. uniform value.

3. Nonviscous flow Roughly speaking. the viscosity 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  s,the

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fluid analog of friction between solids; both are mechanisms by 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, a ship (once set into motion) would not need a propeller!

4. Irrotational flow Although it need not concern us further, we also assume that he flow is irrotational. To test for this property, let a tiny grain uf 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 rotate about an axis through its own center of mass. For a loose analogy, the motion of a Ferris wheel is rotational: that of its passengers is irrotational.

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