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The motion of a fluid is quite complicated. There is something called the Navier-Stokes (NS) equation which is a system of partial differential equations that basically gives the equation of motion for a viscous fluid, but it is very cumbersome to solve, even numerically. NS follows directly from Newton's second law and Newton's law for viscosity (shear stress is proportional to strain rate, and dynamic viscosity ? is the constant of proportionality). There is also something called Euler's equation for fluid motion, which is just NS but with the assumption that viscosity is negligibly tiny.
Fluid mechanics is hard, and so those who study it often rely heavily on emperical relationships and something called dimensional analysis. DA gives us something called the Reynold's number, which is a dimensionles parameter that gives the ratio of inertial forces to viscous. (Re=?VL/? ) When Re is high, like >2000 depending on context, the flow is called turbulent, and Euler's equation ks useful. When it is low, the flow regime is said to be laminar. Then NS is a good description. The really fucky part is what happens in the middle with "transitional" flows.
Hopefully you learned something.
