SUMMARY
The discussion focuses on calculating the shear stress exerted by oil flowing in a horizontal pipe. Given the oil's density of 888 kg/m³ and viscosity of 0.8 Pa·s, the initial calculation of shear stress using the formula τ = -η(dv/dy) resulted in 106.7 Pa. However, the correct shear stress at the pipe wall is 213 Pa, indicating that the velocity gradient is not constant across the pipe. To accurately determine the shear stress, a velocity function v(y) must be derived as a polynomial of degree 2 that satisfies the boundary conditions.
PREREQUISITES
- Understanding of fluid mechanics principles, specifically laminar flow.
- Familiarity with the shear stress formula τ = -η(dv/dy).
- Knowledge of velocity profiles in pipe flow.
- Ability to derive polynomial functions to model flow conditions.
NEXT STEPS
- Study the derivation of velocity profiles for laminar flow in pipes.
- Learn how to calculate shear stress at the wall using velocity functions.
- Explore the implications of non-constant velocity gradients in fluid dynamics.
- Review the application of polynomial functions in modeling fluid flow behavior.
USEFUL FOR
Students and professionals in fluid mechanics, mechanical engineers, and anyone involved in analyzing shear stress in laminar flow scenarios.