1.4. Ideal and Real Fluids
Ideal fluid is defined as the fluid which is incompressible (p = constant) and having no viscosity µ = 0). Ideal fluid is imaginary (because !l’* 0 in any fluid in real word) Real fluid is defined as the fluid which is having viscosity (!l -:t:. 0) and compressible (k -:t:. 0).
1.4.2 Newtonian’s Fluids and Newton’s Law of Viscosity
The property of a fluid which by virtue of it, offers resistance to the motion of layers of fluid is called viscosity. When fluid flows over a solid surface, the velocity is different at different points along the depth. It is zero (no slip) at the solid surface and increases along depth. Fig. 1.2 shows when two layers of a fluid at a distance dry apart, move one over the other at different velocities u and u + du. Layer 2 offers a resistance to layer 1 and vice-versa. The upper layer 2 moving with velocity (u + du) drags the lower layer 1 with velocity u causing a resistance of magnitude F Newton. The shear stress is developed which is F I A where A is the contact area between the two layers. Newton’s law of viscosity states that shear stress is proportional to the spatial rate of change of velocity normal to the flow.
where ’tis the shear stress in N/ m2 , du in m/s, dy in m. So the S.l. unit of µ(called mu)
(coefficient of dynamic viscosity) is given by
The unit of viscosity (.in C.G.S) is poise.
One poise = 0.1 N.s / m2 , µwater = 10-3 Ns / m2
µ air = 1.81 x 10-5 Ns / m2.
The fluid which obeys the law t = µ d u / d y is called Newtonian’s fluid. It is a real fluid.
Water, air, mercury are Newtonian’s fluids.
The fluid which does not obey the law t = µ d u / d y is called Non-Newtonian’s fluid. Paints, polymers, blood are Non-Newtonian’s fluids.
1.4.3 Ideal Plastic Fluid
A fluid which has a definite yield stress and a constant linear relation of t to d u / d y is called ideal plastic fluid. Printers ink and other thixotropic substance are the examples of real plastic fluids, which do not have linear relation of t to du/ dy.
Fig. 1.3 shows rheological diagram for different kinds of fluids.