An ideal water jet with volume flow rate of $$0.05{m^3}/s$$ strikes a flat plane placed normal to its path and exerts a force of $$1000N.$$ Considering the density of water as $$1000$$ $$kg/{m^3},$$ the diameter (in $$mm$$) of the water jet is ____________

In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is $$100$$ $$mm$$ and its tangential speed is $$10$$ $$m/s.$$ The dynamic viscosity of the lubricant is $$0.1$$ $$kg/m.s.$$ The frictional resisting force (in newton) per $$100$$ $$mm$$ length of the bearing is ______________.

For a completely submerged body with center of gravity $$'G'$$ and center of buoyancy $$'B',$$ the condition of stability will be

Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $$30$$ $$mm$$ and thermal conductivity $$15$$ $$W/m.K.$$ At $$x=0,$$ a constant heat flux, $$q'' = 1 \times {10^5}\,\,W/{m^2}$$ is applied. On the other side of the wall, heat is removed from the wall by convection with a fluid at $${25^ \circ }C$$ and heat transfer coefficient of $$250W/{m^2}.K.$$ The temperature (in $${}^ \circ C$$), at $$x=0$$ is ___________