$Q=b{\displaystyle \underset{0}{\overset{h}{}}}v(y)dy$

where $b=10m$ is the width of the channel, $h=3m$ is the overall height of the water in the channel,

and $v(y)$ is the water velocity. The water velocity at some different heights are given in the Table $1.$

$($a$1)$ Using the composite Trapezoidal method to dertermine the flow rate.

$($a$2)$ The typical distribution of the velocity $v(y)$ is shown in Figure $1($b$).$ The shear stress ${}_{xy}$ in the fluid

is described by Newton's equation:

${}_{xy}=\frac{dv}{dy}$

where $=0\mathrm{.}00516N\frac{s}{m^2}$ is the coefficient of dynamic viscosity. The viscosity can be thought of as a

measure of the internal friction within the fluid. Fluids that obey Newton's constitutive equation are called

Newtonian fluids. Calculate the shear stress at $y=0$ using three$-$point forward approximations for the the

derivative.

marks $Q=b{\displaystyle \underset{0}{\overset{h}{}}}v(y)dy$

where $b=10m$ is the width of the channel, $h=3m$ is the overall height of the water in the channel,

and $v(y)$ is the water velocity. The water velocity at some different heights are given in the Table $1.$

$($a$1)$ Using the composite Trapezoidal method to dertermine the flow rate.

$($a$2)$ The typical distribution of the velocity $v(y)$ is shown in Figure $1($b$).$ The shear stress ${}_{xy}$ in the fluid

is described by Newton's equation:

${}_{xy}=\frac{dv}{dy}$

where $=0\mathrm{.}00516N\frac{s}{m^2}$ is the coefficient of dynamic viscosity. The viscosity can be thought of as a

measure of the internal friction within the fluid. Fluids that obey Newton's constitutive equation are called

Newtonian fluids. Calculate the shear stress at $y=0$ using three$-$point forward approximations for the the

derivative.

marks