### Mechanics of Fluids - Short answer questions (Winter 2021)

*Answer the following in brief (4 marks each)*

### Comparison between Newtonian Fluids vs. Non-Newtonian Fluid

Fluids can be classified into two types depending on the viscosity, as Newtonian fluids and non-Newtonian fluids. The key difference between Newtonian and non-Newtonian fluids is that the Newtonian fluids have a constant viscosity, whereas the non-Newtonian fluids have a variable viscosity.

**Newtonian Fluids**

- A fluid which obeys Newton’s law of viscosity is known as a Newtonian fluid.
- Gases and liquid which have simpler molecular formula and low molecular weight are generally come under this.
- The relation between shear stress and shear rate is linear.
- The curve passes through the origin.
- The constant of proportionality is the familiar dynamic viscosity.
- It is time dependent.
- Examples: water, benzene, ethyl alcohol etc.

**Non-Newtonian Fluids**

- A fluid which does not obey Newton’s law of viscosity is known as a Newtonian fluid.
- Material with complex structure and high molecular weight are generally come under this.
- The relation between shear stress and shear rate is not linear.
- The curve may or may not pass through the origin.
- Constant coefficient of viscosity can not be defined.
- It may be time dependent or may not be time dependent.
- Chocolate, ketchup, blood, saliva, toothpaste, paint etc.

### Reynolds Transport Theorem

The Reynolds transport theorem states that the sum of the rate of change of property per unit time for a control volume and rate of efflux of the property are equal to the rate of the change of the extensive property of the system with respect to time. The main function of the Reynold transport theorem is to help to drive the laws of conservation like conservation of momentum, conservation of linear momentum, conservation of mass, conservation of kinetic energy, etc.

Imagine a system and a coinciding control volume with a control surface. Reynolds transport theorem states that the rate of change of an extensive property N, for the system, is equal to the time rate of change of N within the control volume and the net rate of flux of the property N through the control surface. For an example, the law of conservation of mass states that the rate of change of the property, mass, is equal to the sum of the rate of accumulation of mass within a control volume and the net rate of flow of mass across the control surface.

### Friction and Pressure Drag

**Friction drag**

Frictional drag comes from friction between the fluid and the surfaces over which it is flowing. This friction is associated with the development of boundary layers, and it scales with Reynolds number.

**Pressure drag**

Pressure drag comes from the eddying motions that are set up in the fluid by the passage of the body. This drag is associated with the formation of a wake, which can be readily seen behind a passing boat, and it is usually less sensitive to Reynolds number than the frictional drag. It depends on the shape of the body.

Frictional drag is important for attached flows (that is, there is no separation), and it is related to the surface area exposed to the flow. Pressure drag is important for separated flows, and it is related to the cross-sectional area of the body.

For streamlined bodies (like a fish, or an airfoil at small angles of attack), frictional drag is the dominant source of air resistance. For a bluff body (like a brick, a cylinder, or an airfoil at large angles of attack), the dominant source of drag is pressure drag.

### Choked Rayleigh Flow

Rayleigh's flow refers to frictionless, non-adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered. The heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of combustion systems. Heat addition will cause both supersonic and subsonic Mach numbers to approach Mach 1, resulting in

**choked flow**.### Isentropic Stagnation State of Fluid

In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. The isentropic stagnation state is the state a flowing fluid would attain if it underwent a reversible adiabatic deceleration to zero velocity.

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