Calculate the average and maximum velocities of a fluid...

Calculate the average and maximum velocities of a fluid flowing at the rate of $20 \mathrm{~L} / \mathrm{min}$ through a 1.5 -in. sanitary pipe. The fluid has a density of $2030 \mathrm{~kg} / \mathrm{m}^3$ and a viscosity of 50 centipoises. Is the flow laminar or turbulent?

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Key Concepts

Volumetric Flow Rate and Continuity Equation

This concept involves the conservation of mass in fluid flow, where the volumetric flow rate (volume per unit time) is equal to the product of fluid velocity and the cross-sectional area of the pipe. It is fundamental for calculating the average velocity from the given flow rate.

Pipe Cross-Sectional Area Calculation

Calculating the area of a circular cross-section using the diameter (or radius) is essential in fluid mechanics, as it connects the volumetric flow rate to the velocity of flow. The area is typically computed using the formula A = ?*(d/2)².

Average and Maximum Velocity Relationship

For fully developed laminar flow in a circular pipe, the velocity profile is parabolic, meaning the maximum velocity at the center is twice the average velocity. Understanding this relationship helps in determining the maximum velocity once the average velocity is known.

Reynolds Number and Flow Regime

The Reynolds number is a key dimensionless parameter in fluid dynamics that quantifies the ratio of inertial forces to viscous forces. It is used to predict whether the flow is laminar or turbulent, with lower values indicating laminar flow and higher values indicating turbulent flow.

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