CE 230-Engineering Fluid Mechanics Lecture # 28 Laminar flow in circular pipes

Importance of flow in conduits Water and wastewater Agriculture Industry Transport of water or oil Medicine

Flow classification Laminar flow: associated with low velocity and smooth appearance (flow of thick syrup). In pipe flow smooth parabolic velocity distribution. Turbulent flow: intense mixing with variation of velocity with time.

Reynolds apparatus used to study flow type.

Conclusion : Important parameter is Re Laminar flow Re < 2000 Turbulent flow Re > 3000

Laminar flow in circular pipes Objective is to develop 1) the shear stress distribution 2) Velocity distribution 3) A formula for the head loss

Consider a cylindrical element of length Δs and radius r oriented co-axially with the pipe. Consider equilibrium in s direction (steady flow)

But Therefore And shear stress

Determine flow direction and head loss between the two points if the fluid is water. 1 2

h1=200/9.81 =20.39 m h2=110/ =21.21 m Conclusion flow from 2 to 1 Head loss = 0.82 m

Determine flow direction and head loss.

Example 10.1 Example 10.2

Example 10.3 Determine Q if the liquid is kerosene μ = 3.2 x Pa.s, γ= 8010 N/m 3