The Alaskan pipeline, a significant accomplishment of the engineering profession, transports oil 1286 km across the state of Alaska. The pipe diameter is 1.2 m, and the 44 pumps are used to drive the flow. This chapter presents information for designing systems involving pipes, pumps, and turbines.

Typical Applications · For flow in a pipe, find the pressure drop or head loss. · For a specified system, find the flow rate. · For a specified flow rate and pressure drop, determine the size of pipe required. · For a system with a pump, find the pump specifications (power, head, flow rate). · For a specified elevation change and flow rate, find the power that can be produced by a turbine.

1.Development of Pipe Correlation 1.1 Analytical Approach

Viscous Flow in Pipes

Σhl Major Losses 1. Poisueille eq. 2. Darcy’s eq. Minor Losses 1. Sudden expansion 2. Sudden contraction 3. Fittings and valves

Pressure Drop in Laminar Flow The forces on it are: 1- pδA in flow direction 2- p’δA on the reverse direction. 3- friction force acting on its outer-surface. (on the reverse direction of flow) Assumptions incompressible Newtonian one dimen. St.st. Horizontal pipe const. velocity

1.1.1 Force Balance on the Element And assume (p) changes with (l) only .

From boundary conditions: Eq. (8) /(7) 

1.1.2 Relation between v av. & v max :

From (7) in (11)

Example:

1.1.3 Use of friction factor (f) for friction losses determination

For laminar flow sub. Δ P f by Hagen-Poiseuille in Darcy’s eq. : For turbulent flow f = φ( Re, ) ; is roughness factor f is predicted from Moody diagram or fanning diagram

Flow in viscous sub-layer near rough and smooth walls

Colebrook equation graphic representation of Moody Diagram Example: Ans. a) b)

Example: