KNTU CIVIL ENGINEERIG FACULTY ` FLOW IN PIPES With special thanks to Mr.VAKILZADE

Velocity profile: Friction force of wall on fluid open channel pipe

For pipes of constant diameter and incompressible flow V avg stays the same down the pipe, even if the velocity profile changes same V avg same Conservation of Mass

For pipes with variable diameter, m is still the same (due to conservation of mass), but V 1 ≠ V 2 D2D2 V2V2 2 1 V1V1 D1D1 m m

Laminar and Turbulent Flows

Re < 2300  laminar 2300 ≤ Re ≤ 4000  transitional Re > 4000  turbulent Definition of Reynolds number:

Hydraulic diameter: Ac = cross-section area P = wetted perimeter Dh = 4Ac/ P

Consider a round pipe of diameter D. The flow can be laminar or turbulent. In either case, the profile develops downstream over several diameters called the entry length L h. L h /D is a function of Re.

Comparison of: laminar and turbulent flow Instantaneous profiles

slope LaminarTurbulent ww ww  w,turb >  w,lam  w = shear stress at the wall, acting on the fluid

1 2 L ww P1P1 P2P2 V Take CV inside the pipe wall Conservation of Mass

Terms cancel since  1 =  2 and V 1 = V 2 Conservation of x-momentum

or cancel (horizontal pipe) V 1 = V 2, and  1 =  2 (shape not changing) h L = irreversible head loss & it is felt as a pressure drop in the pipe Energy equation (in head form):

 w = func(  V, , D,  )  = average oughness of the inside wall of the pipe

But for laminar flow, roughness does not affect the flow unless it is huge Laminar flow: f = 64/Re Turbulent flow: f = Moody Chart

Minor Losses: K L is the loss coefficient. i pipe sections j components

Energy Line (EL) and Hydraulic Grade Line (HGL) (Source: Larock, Jeppson and Watters, 2000: Hydraulics of Pipeline Systems)

Pipe Networks : Pipes in series Pipes in parallel

1 2 3 AB

Any question?