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.

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of

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