A single pile with 450 mm diameter has been driven into a homogeneous clay layer, which has an undrained cohesion ( $\mathrm{c}_{\mathrm{u}}$ ) of 20 kPa and unit weight of $18 \mathrm{kN} / \mathrm{m}^3$. The ground water table is found to be at the surface of the clay layer. The adhesion factor ( $\alpha$ ) of the soil is 0.95 and bearing capacity factor $\left(N_c\right)$ is 9 . The pile is supporting a column load of 144 kN with a factor of safety of 3.0 against ultimate axial pile capacity in compression.

The required embedment depth of the pile (in m ) is _________ (rounded off to the nearest integer).

Two soils of permeabilities $\mathrm{k}_1$ and $\mathrm{k}_2$ are placed in a horizontal flow apparatus, as shown in the figure. For Soil 1, $L_1=50 \mathrm{~cm}$, and $k_1=0.055 \mathrm{~cm} / \mathrm{s}$; for Soil 2, $L_2=30 \mathrm{~cm}$, and $\mathrm{k}_2=0.035 \mathrm{~cm} / \mathrm{s}$. The cross sectional area of the horizontal pipe is $100 \mathrm{~cm}^2$, and the head difference ( $\Delta \mathrm{h}$ ) is 150 cm . The discharge (in $\mathrm{cm}^3 / \mathrm{s}$ ) through the soils is ________ (rounded off to 2 decimal places).

To derive the total flood hydrograph at a catchment outlet from an isolated storm, the order in which the following methods are applied, from the first method to the last method, is

P. Obtaining the hyetograph

Q. Addition of baseflow

R. Estimation of initial and infiltration losses

S. Application of unit hydrograph

A water resources project with an expected life of 25 years has to be designed for an acceptable risk of $5 \%$ against a design flood. The return period for the design flood (in years) is __________ (rounded off to the nearest integer).