Consider steady flow of water in the series pipe system shown below, with specified discharge. The diameters of Pipes A and B are 2 m and 1 m , respectively. The lengths of pipes A and B are 100 m and 200 m , respectively. Assume the Darcy-Weisbach friction coefficient, $f$ as 0.01 for both the pipes.

The ratio of head loss in Pipe-B to the head loss in Pipe-A is ___________ (round off to the nearest integer).

Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m . The bed slope of the channel is 0.0001 . The Manning roughness coefficient value is 0.02 . Acceleration due to gravity, g can be taken as $9.81 \mathrm{~m} / \mathrm{s}^2$.

The critical depth (in m ) corresponding to the flow rate resulting from the above conditions is ________ (round off to one decimal place).

The drag force, $F_D$ on a sphere due to a fluid flowing past the sphere is a function of viscosity, $\mu$, the mass density, $\rho$, the velocity of flow, $V$ and the diameter of the sphere, $D$.

Pick the relevant (one or more) non-dimensional parameter(s) pertaining to the above process from the following list.

The shaft of a 6 m wide gate in the figure will fail at a moment of $3924 \mathrm{kN} . \mathrm{m}$ about the hinge $P$. The maximum value of water depth $h$ (in $m$ ) that the gate can hold is

___________ (round off to the nearest integer).

Note:

Density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$

Acceleration due to gravity $=9.81 \mathrm{~m} / \mathrm{s}^2$