Hydrostatics: Understanding Fluid Behavior at Rest

This lecture focuses on hydrostatics, the study of fluids at rest. The instructor begins with a recap of the previous week, discussing the definition of a fluid and the no-slip condition related to viscosity. The concept of viscosity is explained, particularly in Newtonian fluids, where shear stress is proportional to shear strain rate. The lecture then transitions into hydrostatics, emphasizing the importance of understanding fluids that do not move. The instructor poses questions about pressure, exploring why it is treated as a scalar rather than a vector. Through a series of logical deductions and examples, the instructor illustrates how pressure acts uniformly in all directions within a fluid element. The lecture culminates in deriving the equation for the pressure field, highlighting the significance of neglecting shear forces in static conditions. The instructor emphasizes the assumptions made during the derivation, ensuring clarity on the conditions under which the results hold true.