Introduction to Fluid Mechanics
Definition of a fluid
A fluid is defined as a substance that deforms continuously under the action of a shear stress,
however small magnitude present. It means that a fluid deforms under very small shear stress,
but a solid may not deform under that magnitude of the shear stress.
Fig.L-1.1a: Deformation of solid under a constant shear force
Fig.L-1.1b: Deformation of fluid under a constant shear force
By contrast a solid deforms when a constant shear stress is applied, but its deformation does not
continue with increasing time. In Fig.L1.1, deformation pattern of a solid and a fluid under the
action of constant shear force is illustrated. We explain in detail here deformation behaviour of a
solid and a fluid under the action of a shear force.
In Fig.L1.1, a shear force F is applied to the upper plate to which the solid has been bonded, a
shear stress resulted by the force equals to,
Where A is the contact area of the upper plate. We know that in the case of the solid block the
deformation is proportional to the shear stress t provided the elastic limit of the solid material is
When a fluid is placed between the plates, the deformation of the fluid element is illustrated in
Fig.L1.3. We can observe the fact that the deformation of the fluid element continues to increase
as long as the force is applied. The fluid particles in direct contact with the plates move with the
same speed of the plates. This can be interpreted that there is no slip at the boundary. This fluid
behavior has been verified in numerous experiments with various kinds
of fluid and boundary material.
In short, a fluid continues in motion under the application of a shear stress and can not sustain
any shear stress when at rest.