Elementary Mechanics of Fluids by Hunter Rouse

By Hunter Rouse

This vintage textual content, nonetheless generic, covers strain edition in sped up circulation, the consequences of gravity and viscosity on fluid movement, theories of floor resistance and shape resistance, elevate and propulsion, floor pressure, position of compressibility in fluid movement and extra. 224 illustrations.

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For example, a long sound wave propagates in a fluid. We do not consider here the external forces that move the fluid; we wish to relate the body velocity u to the fluid velocity v, which is supposed to be homogeneous at the scale of the body size. If the body moved with the same velocity, u = v, then it would be under the action of a force that would act on the fluid in its place, ρV0 v˙ . 3 Flow past a body 27 gives the reaction force dmik (vk −uk )/dt. The sum of the forces gives the body acceleration d d Mui = ρV0 v˙i + mik (vk − uk ).

The phenomenon called separation is responsible for wake creation (Prandtl, 1905). 12. The ideal fluid flow is symmetrical with respect to the plane AB. The point D is a stagnation point. On the upstream half DA, the fluid particles accelerate and the pressure decreases according to the Bernoulli theorem. On the downstream part AC, the reverse happens, that is every particle moves against the pressure gradient. A small viscosity changes pressure only slightly across the boundary layer. Indeed, if the viscosity is small, the boundary layer is thin and can be considered locally flat.

Unfortunately, irrotational flows are much less frequent than Kelvin’s theorem suggests. 5. Yet we shall also see there that large regions of the flow can be unaffected by the vorticity generation and effectively described as irrotational. Another class of potential flows is provided by smallamplitude oscillations (like waves or motions due to oscillations of an immersed body). If the amplitude of oscillations a is small compared with the velocity scale of change l then ∂v/∂t v2 /a while (v∇)v v 2 /l so that the non-linear term can be neglected and ∂v/∂t = −∇W .

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