$1\mathrm{.}1.$ The Lewis number $($Le$)$ is a dimensionless group used to characterise systems with

simultaneous heat and mass transfer. It is composed of four parameters: fluid

density, $,$ fluid specific heat capacity, $c_p,$ fluid thermal conductivity, $k,$ and

molecular diffusivity, $D.$

$Le=\frac{k}{c_{p}D}$

a$)$ A typical thermal conductivity is $k=0\mathrm{.}5W{m}^{-1}{K}^{-1}.$ What are the dimensions of

$k?$

b$)$ The specific heat capacity, $c_p,$ is the proportionality between temperature

change and energy change for a mass $m$ of a substance:

$E=m{c}_{p}T$

What are the dimensions of $c_p?$

c$)$ Diffusivity, $D,$ appears in Fick's second law:

$\frac{dC}{(d)t}=D\frac{d^{2}C}{(d)x^2}$

where $t$ is time, $x$ is distance and $C$ is concentration. What are the dimensions

of $D?$

$1\mathrm{.}2.$ The drag force due to air resistance, $F_D,$ can be expressed as:

$F_D=\frac{1}{2}{v}^2{C}_{D}A$

where $$ is the density of air, $v$ is the velocity of the flow, $C_D$ is a drag coefficient,

and $A$ is the frontal area of the object. Determine the dimensions of the drag

coefficient and its SI units.

$1\mathrm{.}3.$ Newton's law of universal gravitation states that the attractive force between two

masses $m_1$ and $m_2,$ with centre to centre distance $r,$ is

$F=G{m}_1\frac{m_2}{r^2}$

What are the dimensions of $G?$