Mathematics of Fluids and Plasmas 1: Fluid Dynamics module (MA41006)

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Fluid dynamics is the study of the movement of liquids and gases and the forces that affect them. It is a field that explores some of the most captivating and visually stunning phenomena in nature, from the majestic swirls of a tornado to the elegant streamlines of a fluid flowing through a pipe. Fluid dynamics gives us a deeper understanding of the world around us and helps us solve practical problems in engineering, physics, astrophysics, and medicine.   

You will learn how to derive the basic equations of fluid dynamics and how to apply them to solve a variety of mathematical and real-world problems.  

Topics include:  

  • Streamlines, the stream function, and path lines.  
  • Flux and flux tubes.  
  • The continuity equation, hydrostatics, hydrodynamics, and Euler’s equation of motion.  
  • Incompressible, irrotational, potential flows. Bernoulli theorems.  
  • Vorticity, circulation, Kelvin’s circulation theorem, and vorticity evolution.  
  • Viscous flow, the stress tensor, the Navier-Stokes equation, and the Reynolds number.  
  • The solar wind.  
  • Sound waves, linearisation, and dispersion relations.  


This module is available on following courses: