*Answer the following in brief (10 x 2)*

### Define free turbulence and wall turbulence.

**wall turbulence and free turbulence.**

### Give units of mass diffusivity and kinematic viscosity.

### Differentiate between laminar flow and turbulent flow.

- Laminar flows are smooth and streamlined, whereas turbulent flows are irregular and chaotic.
- A low Reynolds number (< 2000) indicates laminar flow while a high Reynolds number indicates turbulent flow. The flow behaviour drastically changes if it is laminar vs. turbulent.

### Write expressions for Fourier’s law of heat conduction and the one-dimensional form of Fick’s law of diffusion.

**Fourier’s law**states that the negative gradient of temperature and the time rate of heat transfer is proportional to the area at right angles of that gradient through which the heat flows. Fourier’s law is the other name of the law of heat conduction.

Where,

q is the local heat flux density in W.m2

k is the conductivity of the material in W.m-1.K-1

▽T is the temperature gradient in K.m-1

**Fick's first law**relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration.

where

J is the **diffusion flux**, of which the dimension is the amount of substance per unit area per unit time. J measures the amount of substance that will flow through a unit area during a unit time interval.

D is the **diffusion coefficient** or **diffusivity**. Its dimension is area per unit of time.

φ (for ideal mixtures) is the concentration, of which the dimension is the amount of substance per unit volume.

x is position, the dimension of which is length.

### Define molecular mass flux and molar flux.

**Molecular mass**

We defined the molecular mass flux of “a ” as the flow of mass of “a ” through a unit area per unit time

In Mathematical expression written as;

j_{a} = ρ_{a}(V_{a} - V)

Here we include only the velocity of species a: relative to the mass average velocity V.

**Molar flux**

The molar flux of species “a" as the no. of moles flowing through a unit area per unit time

In Mathematical expression written as;

j_{a} = C_{a}(V_{a} - V*)

### Write relationships of the friction factor and drag coefficient with Reynolds number in the laminar region.

_{f}= (24/Re) + (4/√Re) + 0.4

### What is Reynolds's analogy?

Reynolds's analogy gives the interrelationship between fluid friction and newton’s law of viscosity.

The Reynolds analogy is given by,

N_{u}/R_{e}P_{r} = S_{t} = C_{f}/2

where

Nu = Local Nusselt number, Re = Local Reynolds number, St = Local Stanton number, Pr = Prandtl number, Cf = Skin friction coefficient

### Define Schmidt number and Grashof number.

**Schmidt number**(Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes.

**Grashof number**(Gr) gives the ratio of buoyant forces to viscous forces and is used to determine the flow regime of fluid boundary layers in laminar systems.

### Define Reynolds number.

### Write a continuity equation for an incompressible fluid.

### Write expressions for terminal settling velocity in Stokes's law regime and Newton’s law regime.

When an object falls through a fluid, it attains a constant velocity through its subsequent motion. This happens because the net force on the body due to gravity and fluid becomes zero.

This constant velocity is termed terminal velocity.

**Stokes law** states that the force of viscosity on a small sphere moving through a viscous fluid is given by:

$F=6πμrv$

Where,

F is the frictional force acting on the interface between the fluid and the particle.

$μ$ is the dynamic viscosity

R is the radius of the spherical object

V is the flow velocity relative to the object

**Newton's law regime**

_{t}= 1.74√(gD

_{p}(ρ

_{1}- ρ

_{2})/ρg

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