Design Example: Flow of Oil Through Circular Pipes

An engineer needs to design a pipeline to transport oil from a storage tank to a processing facility.

Given the oil's viscosity, density, and the pipeline's radius, the goal is to maintain a steady oil flow rate through a circular pipe while ensuring laminar flow to minimize friction and pressure loss.

Using Hagen-Poiseuille's law, the required pressure drop across the pipeline is calculated by considering factors like pipe length, radius, oil viscosity, and the desired flow rate.

This calculation shows the pressure drop needed to achieve the specified flow rate over the pipe's length.

To ensure the flow remains laminar, the Reynolds number, which depends on the oil's velocity, density, and viscosity, is checked.

A Reynolds number below 2100 confirms laminar flow, making Hagen-Poiseuille's law applicable.

Additionally, the maximum velocity at the center of the pipe is estimated verifying that the design meets operational requirements.

This example highlights the significance of pipe radius in determining the flow rate, as even minor adjustments can significantly impact pressure requirements and flow efficiency in pipeline design.