Units of Quantities

1. Kinematic viscosity

v=`mu/rho`= (dynamic viscosity)/(fluid density)`

unit: `m^2s^-1`

2. Dynamic viscosity

`mu=T/gamma`= (sheering stress)/(sheering rate change)

unit:- Pascal second= Pa.s

3. Peclet number

Peclet number, Pe, is a dimensionless group representing the ratio of heat transfer by motion of a fluid to heat transfer by thermal conduction.

Pe= `(uL)/k= Re.Pr`

where, Re= raynolds number; Pr= Prandtl number; u= fluid velocity; L= characteristic dimension;

k= thermal diffusivity

Unit: it is a dimensionless quantity.

4. Nusselt number

The Nusselt number is the ratio of convective to conductive heat transfer across a boundary in a fluid.

Nu= `(hL)/k`

where, h= convective heat transfer coefficient of flow; L= characteristic length; k= thermal conductivity.

unit:- It is a dimensionless quantity.

5. Momentum flux

Momentum Flux is the rate of transfer momentum per unit area.

Formulae:- momentum flux= `(rho.v.vecv)`

where, rho= density of fluid; v= velocity of fluid

unit:- Pascal or `(Kg)/(ms^2)`

6. Fourier's law of heat conduction

This law states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows.

`Q= -kA( (dT) /(dx))`

where, Q= heat flow rate by conduction (W); A= cross sectional area normal to heat flow (`m^2`); k=thermal conductivity of body material; `gradT`=temperature per unit length(`Km^-1`)

unit: Weber(W)

7. Fick's law of diffusion

Fick's first law of diffusion:

`J= -D((d phi)/dx)`

where, J= diffusion flux(amount of substance per unit area per unit time); D= diffusion coefficient(`m^2s^-1`); `phi`=concentration((amount of substance).`m^-3`); x= position(m)

Fick's second law of diffusion:

`(dphi)/dt= D (d^2phi)/dx^2`

`phi`= concentration; t= time; x= position; D= diffusivity

All the dimensions are same as of First law of diffusion.

8. Wall shear stress

`tau(y)= mu(delu)/(dely)`

where, `mu=` dynamic viscosity(Pa.s); u= velocity of the fluid(m/s); y= distance to the wall(m)

`tau(y)`= wall shear stress(Pa)

Unit: pascal(Pa)

9. Gradient of Temperature field

`gradT=((delT)/(delx), (delT)/(dely), (delT)/(delz))`

Unit: Kelvin per meter :(k/m)

10. Divergence of velocity field

velocity field:

`V= uveci +v vecj+ w veck`

Divergence of V:

`grad.V=(delu)/(delx)+(delv)/(dely)+(delw)/(delz)`

Unit: 1/s or `s^-1`