Question $5$

a$.$ Determine, by dimensional analysis, the Drag force $F$ on a sphere $F=f(D,,,v),$ in which $F$ is the

drag force, $D$ is the diameter of the sphere, $$ is the density of the fluid, $$ is dynamic viscosity and $v$

is the velocity of flow.

$[10$ Marks$]$

b$.$ A $100cm$ tall scale model of a proposed $100m$ spillway is used to predict prototype flow conditions.

If the design flood discharge over the spillway is $20,000\frac{m^3}{s}$ and its velocity is $6\frac{m}{s},$ what should

be the water flow rate and velocity tested in the model?

$[6$ Marks$]$

$.$c$.$ Discuss the modelling and types of similarities

$[4$ marks$]$