*Write short notes on the following: (4 marks each)*

### Streak lines and path lines

**Streak Line**

- It is a real line showing instantaneous positions of various particles.
- May change from instant to instant.
- Streak line changes with time. Two streak lines may intersect each other.
- Flow across the streak line is possible.

**Path lines**

A path line is the line traced by a single fluid particle as it moves over a period of time. Thus, a path line indicates the direction of velocity of the same fluid particle at successive instants of time. While a streamline shows the direction of velocity of a number of fluid particles at the same instant of time.

A fluid particle always moves tangent to the streamline thus, for steady flow, the path lines and streamlines are identical.

A fluid particle always moves tangent to the streamline thus, for steady flow, the path lines and streamlines are identical.

### Boundary layer thickness

It is also known as a perpendicular distance between the boundary layer and the solid surface, whereas the boundary layer is the locus of all the points where the velocity is 0.99 times the free stream velocity (u

_{∞}or U).### Applications of Bernoulli’s equations

- Bernoulli’s equation is applied to all problems of incompressible fluid flow.
- The Bernoulli’s equation can be applied to the following measuring devices such as Venturi meter, Nozzle meter, Orifice meter, Pitot tube and its applications to flow measurement within pipes as well as in open channels.
- Bernoulli’s theory is used to study the unstable potential flow.
- It is also employed for the estimation of parameters such as pressure and fluid speed.
- Bernoulli’s principle can be applied in an aeroplane. For example, this theory explains why aeroplane wings are curved upward, and the ships have to run away from each other as they pass.

### Rheopectic and Pseudoplastic fluids

**Rheopectic fluids**

- Rheopectic fluids, such as some lubricants,
**thicken or solidify when shaken**. - Examples of rheopectic fluids include gypsum pastes and printer inks.

**Pseudoplastic fluids**

- Pseudo-plastic fluids are also referred to as shear-thinning fluids. The viscosity of these fluids will decrease with increasing shear rate.
- Examples are examples include quicksand, blood, and milk.

- Newton’s law of viscosity defines the relationship between the shear stress and shear rate of a fluid subjected to a mechanical stress.
- The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity.
- Newtonian fluids obey Newton’s law of viscosity.
- The viscosity is independent of the shear rate.

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