Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is $$6\,\,m{s^{ - 1}}.$$ Then mean velocity (in $$m{s^{ - 1}}$$) of the flow is

A fin has $$5mm$$ diameter and $$100mm$$ length. The thermal conductivity of fin material is $$400W/m K.$$ One end of the fin is maintained at $${130^ \circ }C$$ and its remaining surface is exposed to ambient air at $${30^ \circ }C.$$ if the convective heat transfer coefficient is $$40W/{m^2}K,$$ the heat loss (in $$W$$) from the fin is

Match the following

List-$${\rm I}$$
$$P.$$ Compressible flow
$$Q.$$ Free surface flow
$$R.$$ Boundary layer flow
$$S.$$ Pipe flow
$$T.$$ Heat convection

List-$${\rm II}$$
$$U.$$ Renolds number
$$V.$$ Nussult number
$$W.$$ Weber number
$$X.$$ Froude number
$$Y.$$ Mach number
$$Z.$$ Skin friction coefficient

Annual demand for window frames is $$10000.$$ Each frame costs Rs. $$200$$ and ordering cost is Rs. $$300$$ per order. Inventory holding cost is Rs. $$40$$ per frame per year. The supplier is willing to offer $$2\% $$ discount if the order quantity is $$1000$$ or more, and $$4\% $$ if order quantity is $$2000$$ or more. If the total cost is to be minimized, the retailer should