Bnclear or incomplete answer will result in partial or zero credit.

$R=8\mathrm{.}314$kPa$*d\frac{m^3}{\text{m}\text{o}\text{l}*K},M=29\frac{g}{m}ol(for$ air$)$

$P_{\text{m}\text{i}\text{n}}=101\mathrm{.}3$kPa.

$[2$ marks$]$ Pressure drop $p$ in horizontal circular pipe is given by

$\frac{p}{}=4f(\frac{(L)}{D})\frac{V^2}{2}$

where $$ is the liquid density, $V$ is the average velocity of the fluid, and $L$ and $D$ are the

pipe length and diameter, respectively. The Fanning friction factor f is dimensionless.

Find the SI units $)$ of both sides of the equation.

SI units of $\frac{p}{}=$

SI units of $4f(\frac{L}{D})\frac{V^2}{2}=$

$[2\mathrm{.}5$ marks$]$ A tire having a volume of $0\mathrm{.}081m^3$ contains air at an absolute pressure of

$280$ kPa and a temperature of $21C.$ Calculate the density of the air in $k\frac{g}{m^3}$ and the

mass of the air contained in the tire in kg $.$

Final answers:

Air density $=$

$k\frac{g}{m^3},$

mass of air $=$

kg

$[2\mathrm{.}5$ marks$]$ Consider flow of water in the device shown below, Streams $(1)$ and $(2)$

are both inlet streams.

Using the following information

$A_2=0\mathrm{.}1m^2$;$A_3=0\mathrm{.}3m^2,Q_1=0\mathrm{.}6\frac{m^3}{s}$;$v_2=5\frac{m}{s}$

Calculate $Q_3$ in $m^{\frac{3}{8}}$ and the average velocity v$3$ in section $3$ in $\frac{m}{s}.$

Final answers: $Q_j=$

$m^{\frac{3}{s}},v{a}_3=$

$\frac{m}{s}$

$[4$ marks$]$ A laminar flow occurs between two horizontal plates under a pressure

gradient. The upper plate moves left at velocity $u_f.$ The expression for local velocity is

given as

$u=-a(Hy-y^2)+u_1\frac{y}{H}$

where a and $u_t$ are constant.

a$)[1$ mark$]$ Using the above expression, Prove that the two no$-$slip boundary conditions

are satisfied.

Boundary condition $1$: