Couette flow is characterized by

Three parallel pipes connected at the two ends have flow-rates $$\,\,\,{Q_1},\,\,\,{Q_2},\,\,\,\,$$ and $${Q_3}$$ respectively, and the corresponding frictional head losses are $${h_{L1}},\,\,\,{h_{L2}},$$ and $${h_{L3}}$$ respectively. The correct expressions for total flow rate $$(Q)$$ and frictional head loss across the two ends $$\left( {{h_L}} \right)$$ are.

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

The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression. $$$u\left( r \right) = {{ - {R^2}} \over {4\mu }}\left( {{{dp} \over {dx}}} \right)\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$$
Where $${{dp} \over {dx}}$$ is a constant.

The average velocity of fluid in the pipe is