Question $1$

$($a$)$ In a fluid the velocity measured at a distance of $70$ mm from the boundary is

$1\mathrm{.}5\frac{m}{s}.$ The fluid has dynamic viscosity $0\mathrm{.}048$ Pa $-$s and specific gravity

$0\mathrm{.}913.$ What is the velocity gradient and shear stress at the boundary

assuming a linear velocity distribution?

$5$ Marks

$($b$)$ How deep can a diver descend in sea water without damaging his watch,

which can withstand an absolute pressure of $5\mathrm{.}5$ bar? Take the density of

ocean water $=1025k\frac{g}{m^3}.$

$3$ Marks

$($c$)$ Show that the kinematic viscosity has the primary dimensions of $L^2{T}^{-1}.$

$2$ Marks

$($d$)$ A $20$ mm diameter pipe branches into two pipes, one branch being $10$ mm in

diameter and the other $15$ mm in diameter. If the velocity in the $10$ mm pipe

is $0\mathrm{.}3\frac{m}{s}$ and that in the $15$ mm pipe is $0\mathrm{.}6\frac{m}{s},$ calculate the rate of flow in

the $20$ mm diameter pipe.

$5$ Marks

$($e$)$ Oil of specific gravity of $0\mathrm{.}90$ flows at the rate of $100k\frac{g}{s}$ in a horizontal pipe

of $200$ mm diameter and $1$ km long. If the friction factor for the pipe is $0\mathrm{.}006,$

calculate the frictional head loss in the pipe.

$5$ Marks

$($f$)$ Estimate the total minor losses in a straight pipeline of $3$ m long and $50$ mm

diameter, discharging water into the atmosphere at a rate of $0\mathrm{.}0025\frac{m^3}{s}.$

The pipe has sharp entrance and exit.

$5$ Marks