The word fluid means a substance having particles which readily of its magnitude (a small shear stress, which may appear to be of negligible will cause deformation in the fluid). Fluids are charactrised by such properties as density. Specific weight, specific gravity, viscosity etc. Density of a substance is defined as mass per unit volume and it is denoted by. The specific gravity represents a numerical ratio of two densities, and water is commonly taken as a reference substance. Specific gravity of a substance in written as the ratio of density of substance to the density of water. Specific weight represents the force exerted by gravity on a unit volume of fluid. It is related to the density as the product of density of a fluid and acceleration due to gravity. Viscosity is the most important and is recognized as the only single property which influences the fluid motion to a great extent. The viscosity is the property by virtue of which a fluid offers resistance to deformation under the influenece if shear force. The force between the layers opposing relative motion between them are known as forces of viscosity. When a boat moves slowly on the river remains at rest. Velocities of different layers are different. Let `v` be the velocity of the level at a distance `y` from the bed and `V+dv` be the velocity at a distance `y+dy`. The velocity differs by `dv` in going through a distance by perpendicular to it. The quantity `(dv)/(dy)` is called velocity gradient. The force of viscosity between two layers of a fluid is proportional to velocity gradient and Area of the layer.
`F prop A` & `F prop (dv)/(dy)`
`F= -etaA(dv)/(dy)` (`-ve` sign shown the force is frictional in nature and opposes relative motion. `eta` coefficient of dynamic viscosity
Shear stress `(F)/(A)= -eta(dv)/(dy)`
and simultaneously kinematic viscosity is defined as the dynamic viscosity divided by the density. If is denoted as `v`. The viscosity of a fluid depends upon its intermolecular structure. In gases, the molecules are widely spaced resulting in a negligible intermolecular cohesion, while in liquids the molecules being very close to each other, the cohesion is much larger with the increases of temperature, the cohesive force decreases rapidly resulting in the decreases of viscosity. In case of gases, the viscosity is mainly due to transfer of molecular momentum in the transerve direction brought about by the molecular agitation. Molecular agitation increases with rise in temperature. Thus we conclude that viscosity of a fluid may thus be considered to be composed of two parts, first due to intermolecuar cohesion and second due to transfer of molecular momentum.
If the velocity profile is given by
`v=(2)/(3)y-y^(2)v` is velocity in `m//sec y` is in meter above the bad. Determine shear stress at `y=0.15m`, & `eta=0.863 Ns//m^(2)`

Options

A. `0.316`
B. `0.45`
C. `0.50`
D. `0.63`