This lesson covers the topic of experimental methods in fluid mechanics, focusing on displacement and area measurement. It delves into the use of a pneumatic displacement gauge to measure small distances, explaining the construction details and the mathematical equations involved. The lesson also discusses the concept of pneumatic displacement gauge sensitivity and how it is affected by supply pressure and diameter ratio. The second part of the lesson introduces the polar planimeter, a mechanical instrument used for area integration. It explains how the planimeter works, its accuracy, and the factors that influence it. The lesson concludes with a brief mention of numerical methods for finding the area under a curve.
00:37 - Pneumatic displacement gauge
14:22 - Pneumatic displacement gauge sensitivityn
30:36 - Introduction to the polar planimeter
32:46 - Explanation of how the polar planimeter works
45:57 - Accuracy of the polar planimeter
- A pneumatic displacement gauge is used to measure small displacements and its sensitivity depends on the diameter ratio and supply pressure.
- The polar planimeter is a mechanical instrument used for area integration. Its accuracy depends on the accuracy of the boundary drawn, the resolution of the counter, and the skill at tracing the boundary.
- Numerical methods such as the Trapezoidal rule, Simpsons rule, and Gaussian quadrature are available for finding the area under a curve.