Hydraulics & Fluid Mechanics
Two pipe systems are said to be equivalent when

length of pipe and discharge are same in two systems
length and diameter are same in two systems
friction factor and length are same in two systems
head loss and discharge are same in two systems

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Hydraulics & Fluid Mechanics
For laminar flow in a pipe of circular cross-section, the Darcy’s friction factor f is

inversely proportional to Reynolds number and indpendent of pipe wall roughness
directly proportional to pipe wall roughness and independent of Reynolds number
inversely proportional to Reynolds number and directly proportional to pipe wall roughness
directly proportional to Reynolds number and independent of pipe wall roughness

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Hydraulics & Fluid Mechanics
According to Bernoulli’s equation for steady ideal fluid flow

total energy is constant throughout
velocity and pressure are inversely proportional
principle of conservation of mass holds
the energy is constant along a stream-line but may vary across streamlines

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