Fluid Mechanics and Machinery
Fluid: Fluid is a substance which has the property tendency to flow under the action of shear and tangential forces.
Liquids and gases both are fluids.
Ideal and Real fluids:
- In ideal fluids, there is no viscosity and no surface tension and are incompressible.
- In real fluids, viscosity, surface tension together exist and are compressible along with density.
Classification of fluids:
Fluids can be classified on the basis of the following:
Based on density and viscosity
(i) Ideal fluid: An ideal fluid is described as a fluid which is in compressible and also has zero viscosity and constant density.
(ii) Real fluids: A real fluid is described as a fluid which is compressible and viscous by nature. The density of real fluid are variable and while in motion, an amount of resistance is always offered by these fluids.
(iii) Newtonian fluids: Newtonian fluidss are denned as fluids those obey Newton's law of viscosity. The density of these fluids may be constant or variable. The viscosity is calculated according to Newton'.s law of viscosity as:
\[\tau =\mu \frac{du}{dy}\]
where, \[\tau \]=shear stress
\[\mu =\]viscosity of fluid
\[du/dy=\]velocity gradient
Examples are, water, ethyl alcohol, benzene etc.
(iv) Non – Newtonion fluids: Non-newtonian fluids are defined as fluids those do not obey Newton's laws of viscosity.
The density of these fluids may be constant or variable and the viscosity of these fluids does not remain constant.
Examples are Gels, Solutions of polymers, pastes etc.
(v) Compressible fluids: A compressible fluid is defined as the fluid which reduces its volume when an external pressure is applied. All the fluids available in nature are compressible.
(vi) In–compressible fluids: Incompressible fluids are defined as the fluids whose density does not change when the value of pressure changes. There is no effect of pressure on the density of fluid. In these fluids, density remains constant and viscosity remains non-zero.
(vii) Inviscid fluid: Inviscid fluid is the fluid which has zero iscosity and density may be constant or variable.
FLUID PROPERTIES
Density\[(\rho )\]: It is denned as mass per unit volume of substance.
\[\rho =\frac{m}{V}\]
Specific Weight\[(\omega )\]: It is defined as weight per unit volume of substance.
\[\omega =\frac{mg}{V}=\rho g\]
Relative density Specific gravity (Sg): It is defined as ratio of density of fluid to the density of standard fluid.
It may also be defined as the ratio of specific weight of the fluid to the standard weight of fluid.
\[\text{Sg=}\frac{\text{weogjt}\,\,\text{of}\,\,\text{fluid}}{\text{weight}\,\,\text{of}\,\,\text{standard}\,\,\text{fluid}}\]
\[\text{Sg=}\frac{\text{Density}\,\,\text{of}\,\,\text{fluid}}{\text{Density}\,\,\text{of}\,\,\text{standard}\,\,\text{Fluid}}\]
Ex: oil of Sg of 0.8\[\Rightarrow {{\rho }_{oil}}=800\,\,kg/{{m}^{3}}\]
Specific volume (v):
It is expressed as the volume per unit mass of fluid.
\[v=\frac{V}{m}=\frac{1}{\rho }\]
Compressibility \[(\beta )\]
Hydrostatic law: It states that rate of increase of pressure in a vertical direction is equal to weight density of fluid at that point.
Mathematically, pressure head (h)\[(h)=\frac{\rho }{\rho g}\]
\[\beta =\frac{-\frac{dV}{V}}{dp}=\frac{1}{\rho }\,\,\frac{d\rho }{dp}\]
Liquids are highly incompressible.\[\therefore \,\frac{d\rho }{dp}=0\]
Gases are highly compressible as \[P\propto \rho
more...