FM-Class-6-Summary

MSubbu led a session on fluid mechanics, covering 24 representative questions from the GATE Chemical syllabus. He explained key concepts including pressure at the bottom of containers, force on dam sides, and pressure balance in manometers. MSubbu emphasized the importance of understanding basic principles rather than getting distracted by complex calculations, and highlighted that the session focused primarily on GATE Chemical topics.

MSubbu discussed buoyancy-related problems, including calculating the force required to hold a solid body in water and solving hydrometer problems. He explained the concepts of net downward forces, buoyancy, and gravity, and demonstrated how to find the mass of fluid displaced and the density of the body. MSubbu also mentioned that the body is capable of floating due to its lower density compared to water. He then moved on to fluid flow problems and reminded the students about the importance of attending classes regularly.

MSubbu explained different types of fluid behavior, including Newtonian, Bingham plastic, pseudoplastic, and dilatant fluids, using stress versus strain rate relationships. He described how pseudoplastic fluids exhibit shear thinning (decreasing viscosity with increasing strain rate) and dilatant fluids exhibit shear thickening (increasing viscosity with increasing strain rate). MSubbu also explained how to determine the type of fluid based on the power law model and apparent viscosity, noting that pseudoplastic fluids have n < 1, while dilatant fluids have n > 1.

MSubbu discussed the conditions under which Bernoulli's equation is applicable, emphasizing that it requires steady-state, incompressible, and inviscid flow. He explained that while irrotational flow is not a requirement, irrotational flow leads to potential flow, which adds another condition for potential flow situations. MSubbu also covered the concept of ideal fluid flow, noting that it has a Reynolds number of infinity and can be assumed for flows like air through pipelines where pressure drop is low. He concluded by mentioning that questions about the applicability of Bernoulli's equation are commonly seen in GATE-AE questions.

MSubbu explained the principles of fluid flow through pipelines, focusing on the relationship between pressure and velocity. He discussed how a diverging pipeline can lead to increased pressure and decreased velocity, and how this can cause boundary layer separation and energy loss if not properly managed. MSubbu also compared the performance of Venturi meters and orifice meters, explaining that Venturi meters have a higher flow coefficient and lower energy losses, so when replacing a Venturi meter with an orifice meter, a larger manometer with a greater pressure difference is needed to measure the same flow rate.

MSubbu discussed various aspects of fluid mechanics, including friction factors, Reynolds numbers, and flow regimes. He explained the relationships between velocity profiles, shear stress, and pressure drop for laminar and turbulent flows. MSubbu also covered the concept of equivalent diameter for non-circular cross-sections and the calculation of power required for pumping. Finally, he addressed the topic of drag and settling velocities, discussing the relationships between terminal velocity and particle diameter in different flow regimes.

MSubbu completed the Fluid Mechanics portion of the course and announced plans for upcoming sessions. He will post a test for each topic before the next mechanical operations class, which will be 1.5 hours long on Sunday. MSubbu mentioned that 20% of the syllabus will be covered by then, and the entire syllabus (60% of GATE-CH) will be completed by August 14th. 

MSubbu emphasized the importance of taking tests after completing each portion to build confidence, and he shared a simple formula for solving Fluid Mechanics problems using the Bernoulli equation, and \(\Delta P = 2fL\rho v^2/D\)