Fluid Dynamics

how fluids flow

All fluids are viscous, but for water, it is negligible (pressure X time) or NsXm^2 Momentum divided by surface area

Viscosity increase. They have an inverse relationship

A flowing fluid is composed of parallel layer that may be moving at different velocities Poiseuille’s law (accounts for viscosity) Q=pir^4changeP / 8nL changeP=8nLQ/pir^4

Flowing fluid composed of mixed layers that vary dramatically in pressure and speed a “mess” represented by Reynolds number Re = (density X velocity X diameter) / dynamic viscosity fluid

Higher velocity= more likely the flow is to become turbulent

Q is proportional to changeP changeP is proportional to L 1/L is proportional to Q Q is proportional to r^4 (so increasing radius will increase flow rate)

highly idealized fluids • assume laminar flow • neglect viscosity • neglect interactions between the fluid and container

P1 + 1/pv^2 + pgh = P2 + 1/pv^2 + pgh Three terms on each side P= pascals kinetic energy potential energy pressure = energy/volume and this is what this equation boils down to

at a constant height, increasing the velocity will decrease the pressure exerted on the container

Within a closed system, the flow rate of a liquid is constant (Q1=Q2) Q=V*A liquids are incompressible

To get a volume to flow through a narrow section compared to a wider section, it’ll need to be faster

linked to velocity pitot tube = one ended tube, stagnation pressure measure speed of airplanes, ship, wind difference between stag and static = 1/2pv^2