Water flows through a pipe of diameter $$0.30$$ $$m.$$ What would be the velocity $$V$$ for the conditions shown in the figure below?

A circular plate $$1$$ $$m$$ in diameter is submerged vertically in water such that its upper edge is $$8m$$ below the free surface of water. The total hydrostatic pressure force on one side of plate is :

A Newtonian fluid has the following velocity field : $$$\overrightarrow V = {x^2}y\widehat i + 2x{y^2}z\widehat j - y{z^3}\widehat k$$$

The rate of shear deformation $${\varepsilon _{yz}}$$ at the point $$x=-2, y=-1$$ and $$z=2$$ for the given flow is :

Steam is flowing through an insulated steel pipe shown in the fig, is losing heat to the surroundings. The details are as follows

Inner radius of steel pipe $$=50mm,$$
Outer radius of the steel pipe $$=57mm,$$
Outer radius of insulation $$=157 mm,$$
Thermal conductivity of steel $$=43$$ $$W/mK$$
Thermal conductivity of insulating material $$=0.1$$ $$W/mK$$
Heat transfer coefficient on steam side $$ = 570W/{m^2}K$$
Heat transfer coefficient on air side $$ = 12W/{m^2}K,$$
Temperature of steam $$ = {500^ \circ }C$$
Temperature of surroundings $$ = {30^ \circ }C$$

Calculate the heat loss per meter length of pipe and temp of the outer surface of the insulation.