Units of quantities

Basic quantities with units

1. Kinematic viscosity (ν)

- Kinematic viscosity is defined as ratio of dynamic viscosity per unit density.

ν = μ/ρ

Unit of Kinematic viscosity is m²/s.

As

μ = dynamic viscosity (N-s/m²)

ρ = density (kg/m³)

1. Dynamic viscosity (µ)

- Dynamic viscosity is the tangential force required to move one horizontal plane with respect to another plane at a unit velocity while maintaining a unit distance in the fluid.

μ = τ / y

τ = Shear Stress (N/m²)

y = ∂u/∂y = rate of change of shear stress

1. Peclet number (Pe)

- It is the ratio of advective transport rate to diffusive transport rate in a fluid.

Expression: Pe (L) = Re (L) * Pr

Re = Reynolds number

Pr = Prandtl number

This number is dimensionless, thus it has no unit.

1. Nusselt number (Nu) – It is the ratio of convective to conductive heat transfer across the boundary.

Nu = h.L/k

It is a dimensionless number hence there is no unit.

1. Momentum flux (p) -

Momentum flux is the rate of change of momentum per unit normal area in the direction of flow or Force per unit area normal to the direction of flow.

F = Force (N)

A = Area (m2)

p = F/A

SI Unit: N/m²

1. Fourier\'s law of heat conduction -

- It states that the rate of heat transfer through a material is directly proportional to the negative gradient of the temperature and the cross sectional area through which heat flows.

Q = Rate of heat flow by Conduction. (W)

k = constant of thermal conductivity. (W/mK)

A = Cross sectional area of the material. (m²)

dT/dx = Temperature Gradient. (K/m)

Therefore,

Q = -k.A(dT/dx)

1. Fick\'s law of diffusion –

Fick’s law of diffusion states that the molar flux due to diffusion is proportional to the concentration gradient.

N= molar flux

c = Concentration Gradient.

D = diffusion coefficient.

N = c.D

1. I unit is mol/m²-s

1. Wall shear stress (τ)

- It is the force per unit area acting parallel to the flow direction or wall between two fluid layers or between a fluid and a solid wall.

Expression: Tau = (μ)* (dU/dy)

(μ) - Dynamic viscosity

U - velocity in the direction of flow

y - distance to wall

SI Unit: Pascal (Pa)

1. Gradient of Temperature field:

- Gradient of temperature field is the quantity that defines the variation of temperature in a particular direction. It signifies how rapidly or slowly the temperature is changing in a specific direction.

Expression: dT/dx = [T(x) - T(o)] / [x(2) - x(1)]

Unit: K/m (kelvin per meter)

1. Divergence of velocity field:

-Divergence of the velocity field (U) is the scalar quantity that signifies how much the velocity is diverging around a given point.

Expression: div(U) = dU/dx + dU/dy + dU/dz

Divergence is a dimensionless quantity.