At a municipal waste handling facility, 30 metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be 10%. The ideal moisture content for composting this mixture is 50%. The amount of water to be added to this mixture to bring its moisture content to the ideal condition is _________ metric ton. (in integer)

The concentration s(x, t) of pollutants, in a one-dimensional reservoir at position x and time t satisfies the diffusion equation

$${{\partial s(x,t)} \over {\partial t}} = D{{{\partial ^2}s(x,t)} \over {\partial {x^2}}}$$

on the domain 0 $$\le$$ x $$\le$$ L, where D is the diffusion coefficient of the pollutants. The initial condition s(x, 0) is defined by the step-function shown in the figure.

The boundary conditions of the problem are given by $${{\partial s(x,t)} \over {\partial x}}$$ = 0 at the boundary points x = 0 and x = L at all times. Consider D = 0.1 m²/s, s₀ = 5 $$\mu$$mol/m and L = 10 m. The steady-state concentration $$\overline s \left( {{L \over 2}} \right) = s\left( {{L \over 2},\infty } \right)$$ at the center x = $${{L \over 2}}$$ of the reservoir (in $$\mu$$mol/m) is __________. (in integer)

Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. Assume Stoke's law is valid.

The drag force on particle Q will be ___________ times the drag force on particle P. (round off to the nearest integer)

A hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m³/s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is _________. (round off to two decimal places)

(Consider the acceleration due to gravity as 10 m/s².)