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

In fully developed laminar flow in the circular pipe, the head loss due to friction is directly proportional to ....... (Mean velocity/square of the mean velocity)