Laminar Flow: Problem Solving

Consider air flowing through the pipe at 300 Kelvin at standard atmospheric pressure, with a mass flowrate of 0.0163 kilograms per second. If the flow is assumed to be laminar, determine the minimum diameter allowed for the pipe.

Laminar flow is achieved when the Reynolds number does not exceed 2100. This calculation begins by expressing the velocity in terms of flow rate and cross-sectional area.

For a circular pipe, the velocity depends on the flow rate and the pipe's diameter. Substituting this expression for velocity into the Reynolds number formula, which involves density, velocity, diameter, and viscosity, allows solving for the flow rate.

Given the specified flow rate, the fluid density is calculated using known values for pressure, gas constant, and temperature, yielding approximately 1.177 kilograms per cubic meter.

With the known quantities of mass flowrate and density, the volumetric flow rate is found to be around 0.0138 cubic meters per second.

Using a standard viscosity value, the required pipe diameter to ensure laminar flow is approximately 0.46 meters, keeping the Reynolds number at 2100.