Consider laminar flow of water over a flat plate of length $$1$$ $$m.$$ If the boundary layer thickness at a distance of $$0.25$$ $$m$$ from the leading edge of the plate is $$8$$ $$mm,$$ the boundary layer thickness (in $$mm$$), at a distance of $$0.75$$ $$m,$$ is __________________

A fluid of dynamic viscosity $$2 \times {10^{ - 5}}\,\,kg/m.s$$ and density $$1kg/{m^3}$$ flows with an average velocity of $$1$$ $$m/s$$ through a long duct of rectangular $$\left( {25\,\,mm \times \,\,15\,\,mm} \right)$$ cross-section. Assuming laminar flow, the pressure drop (in $$Pa$$) in the fully developed region per meter length of the duct is __________________.

Water flows through a pipe having an inner radius of $$10$$ $$mm$$ at the rate of $$36$$ $$kg/hr$$ at $${25^ \circ }C$$. The viscosity of water at $${25^ \circ }C$$ is $$0.001$$ $$kg/m.s.$$ The Reynolds number of the flow is ____________________

For a fully developed flow of water in a pipe having diameter $$10$$ $$cm,$$ velocity $$0.1$$ $$m/s$$ and kinematic viscosity $${10^{ - 5}}\,\,{m^2}/s,$$ the value of Darcy friction factor is ________________