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The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms. In analyzing flow through a pipe, variables that define the system include the pipe's diameter, the fluid's velocity, its density, and viscosity. These can be combined into a single dimensionless term, the Reynolds number (Re), which captures their essential relationship. The first step in applying the Buckingham Pi theorem is identifying...

The Buckingham Pi theorem is a valuable method in dimensional analysis, reducing complex relationships between variables into dimensionless terms. Relevant variables in analyzing the lift force on an airplane wing include lift force, air density, wing area, aircraft velocity, and air viscosity. Expressing each variable in terms of fundamental dimensions — mass, length, and time — provides a consistent foundation for constructing these dimensionless terms. The theorem indicates that the number...

Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...

Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy. Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...

Here, we present an overview of the preparation and animal handling procedures required to safely perform medical imaging in an animal biosafety level 4 laboratory. Computed tomography of a mock-infected guinea pig illustrates these procedures that may be used to evaluate the disease caused by a high consequence pathogen.