Fluid Mechanics

Fluid mechanics is categorises into three section

a)     Kinematics - Study of motion without taking help of force.

b)     Dynamics - Study of motion with taking help of force.

c)     Statics – Study of fluid mechanics in which fluid particles are at rest.

Fluid – A fluid is a substance which continuously deforms under the action of tangential / shears forces.

This continuous definition of the fluid in other terms is known as flow of the fluid.

Properties - There are two different types of properties

a)     Intensive - Independent of mass

b)     Extensive - Dependent of mass

Density – Mass per unit volume. Density is intensive property.

Note – Extensive properties per unit mass become intensive properties.

Specific Gravity – It is defined as the ratio of density of the substance to density of the standard substance. For liquid standard substance is water at 4 ºC and for gas standard substance is air. Specific gravity of water is 1.

Relative Density – It is defined as the ratio of density of the substance to the density of other substance.

(R.D)2/1 = ρ2/ρ1

Specific Weight – It is the weight of the fluid element per unit volume.

                                     Sp. Weight = m.g/v = ρ.g

Viscosity - The two adjacent layers of the fluid resist the motion of each other, this very important property of the fluid is known as viscosity. It is the measurement of the internal resistance between the layers of the fluid.

Newton’s Law of Viscosity:

Angular deflection of fluid element:

tan dθ= du x dt/dy, For very small angle tan θ = θ

So dθ = du x dt/dy, or (dθ/dt) =(du/dy)---------------------------------------------------(1)

i.e rate of angular deformation or rate of shear deformation is equal to velocity gradient in the perpendicular direction.

Newton’s Law:

Shear stress is directly proportional to rate of shear deformation

Ʈ directly proportional to (dθ/dt) from equation (1)

Ʈ=µ(du/dy)

 µ=Property of the fluid, for the same fluid it is function of temperature.

Analysis of µ:

µ less means (du/dy) more – means (dθ/dt) is more means easy to flow

Ʈ less means less internal resistance

µ more means (du/dy) less – means (dθ/dt) is less means difficult to flow

Ʈ high means more internal resistance