A $$0.20$$ $$m$$ diameter pipe $$20$$ $$km$$ long transport oil at a flow rate of $$0.01{m^3}/s.$$ Calculate the power required to maintain the flow if the dynamic viscosity and density of oil are $$0.08$$ $$Pa$$-$$sec$$ and $$900\,kg/{m^3}.$$

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

The parameters which determines the friction factor for turbulent flow in a rough pipe are:

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 :