Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $$\mu $$ through a circular pipe of radius $$R.$$ Given that the velocity at a radial location of $$R/2$$ from the center-line of the pipe is $${U_1},$$ the shear stress at the wall is $$K\mu {U_1}/R,$$ where $$K$$ is _________________.

A channel of width $$450$$ $$mm$$ branches into two sub-channels having width $$300$$ $$mm$$ and $$200$$ $$mm$$ as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $$0.9$$ $$3$$ $$m/s,$$ and the velocity in the sub-channel of width $$200$$ $$mm$$ is $$3$$ $$m/s,$$ the velocity in the sub-channel of width $$300$$ $$mm$$ is _____________ $$m/s$$.

Assume both inlet and outlet to be at the same elevation.

For a certain two-dimensional incompressible flow, velocity field is given by $$2xy\widehat i - {y^2}\widehat j.$$ The streamlines for this flow are given by the family of curves

Steady one-dimensional heat conduction takes place across the faces $$1$$ and $$3$$ of a composite slab consisting of slabs $$A$$ and $$B$$ in perfect contact as shown in the figure, where $${k_A},\,\,{k_B}$$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $${T_2}$$ $$\left( {in\,{\,^ \circ }C\left. \, \right)} \right.$$ is ______________.