Fluid mechanics: Viscosity, Poiseuille's law, venturi tube

Fundamental concepts in fluid mechanics.
Viscosity is the resistance that a fluid offers to movement and deformation. It is measured in Pascal-seconds (Pa·s).
Poiseuille's Law
Poiseuille's law describes the laminar flow of viscous fluids in cylindrical tubes:

Q = (π × r^4) / (8 × η × L) × ΔP

where:

1. Q is the flow
2. r is the radius of the tube
3. η is the viscosity
4. L is the length of the tube
5. ΔP is the pressure difference
Venturi tube
The Venturi tube is a device that reduces the cross section of a tube, increasing the velocity of the fluid and decreasing the pressure.
Reynolds number
The Reynolds number (Re) characterizes the flow regime:

Re = ρ × v × d / η

where:

1. ρ is the density of the fluid
2. v is the speed
3. d is the diameter of the tube
4. η is the viscosity

Flow regimes
1. *Laminar*: Re < 2000
2. *Transitional*: 2000 < Re < 4000
3. *Turbulent*: Re > 4000
Applications
1. *Hydraulic engineering*: Design of irrigation and sewage systems.
2. *Mechanical engineering*: Design of machines and fluid systems.
3. *Medicine*: Study of blood flow.
4. *Aerodynamics*: Study of air flow.
Units
1. *Pascal-seconds (Pa·s)*: Unit of viscosity.
2. *Reynolds (Re)*: Dimensionless.
Importance
1. *Efficient design*: Of fluid systems and machines.
2. *Safety*: Avoid pressure and flow losses.
3. *Innovation*: Development of advanced technologies.