Midterm-Review GLY-5835 Basic Fluid Dynamics Momentum p = mv F = dp/dt = m dv/dt Viscosity Resistance to flow; momentum diffusion Low viscosity: Air High viscosity: Honey Kinematic viscosity Poiseuille Flow In a slit or pipe, the velocities at the walls are 0 (no-slip boundaries) and the velocity reaches its maximum in the middle The velocity profile in a slit is parabolic and given by: x = 0x = a u(x) G can be gravitational acceleration or (linear) pressure gradient (P in P out )/L Entry Length Effects Reynolds Number The Reynolds Number (Re) is a non-dimensional number that reflects the balance between viscous and inertial forces and hence relates to flow instability (i.e., the onset of turbulence) Re = v L/ L is a characteristic length in the system Dominance of viscous force leads to laminar flow (low velocity, high viscosity, confined fluid) Dominance of inertial force leads to turbulent flow (high velocity, low viscosity, unconfined fluid) Re