Flow in Closed Circular Conduits

Study Notes

Laminar Flow: occurs at low velocities, fluid molecules move in an orderly fashion, no mixing of fluid particles, and fluid velocity is maximum at the center of the pipe and zero at the pipe wall.
Turbulent Flow: occurs at relatively high velocities, eddy currents are formed, mixing of fluid particles occurs, and fluid particles have a random motion transverse to the main flow direction.
Transition Flow: occurs when velocity is between laminar and turbulent flow, a transition stage when the flow cannot be classified as laminar or turbulent flow.

Reynolds Number is a dimensionless parameter that determines the type of fluid flow through pipes.
It is dependent on four factors: average velocity of the fluid (v), pipe diameter (d), dynamic viscosity of the fluid (μ), and density of the fluid (ρ).
The Reynolds Number is calculated by: Re = ρvd/μ.
Laminar flow exists at low Reynolds Numbers (Re ≤ 2000), turbulent flow exists at high Reynolds Numbers (Re ≥ 4000), and transition flow exists when 2000 < Re < 4000.

Reynolds Number classification:
- Re < 2000: Laminar Flow
- Re > 4000: Turbulent Flow
- 2000 < Re < 4000: Transient Flow

Hydraulic radius (R) is the characteristic dimension for flow path in non-circular cross-sections.
R is defined as the ratio of the cross-sectional area (A) to the wetted perimeter (WP).
Wetted perimeter (WP) is the sum of the length of boundaries in contact with the fluid.
The unit for R is meters (SI unit system) or feet (U.S. Customary System).

For a non-circular cross-section, R can be calculated using the formula: R = A / WP
A is the net cross-sectional area of the flow stream
WP is the wetted perimeter

The Reynolds number (Re) for flow in non-circular sections is computed by replacing the diameter (d) with 4R, i.e., four times the hydraulic radius.
The formula for Re is: Re = ρv(4R) / μ
ρ is the fluid density, v is the fluid velocity, and μ is the fluid dynamic viscosity.

The validity of this substitution can be demonstrated by calculating the hydraulic radius for a circular pipe.
This approach will give reasonable results if the cross-section has an aspect ratio (ratio of the width of the section to its height) not much different from that of the circular cross-section.