Fluid Mechanics

SI units & Physics constants

Fluid mechanics investigates motion of objects in fluid media

Here (all units see here):

A₁ and A₂ are cross section areas of tube at sections 1 and 2 respectively

v₁ and v₂ are velocities of fluid at sections 1 and 2 respectively

P₁ and P₂ are static pressures at sections 1 and 2 respectively

h₁ and h₂ are heights of center of sections 1 and 2 respectively above the earth surface

 is density of fluid

General formulas

Pressure in fluid

where  is normal component of force acting from the fluid on small plane with area  placed in the fluid

Density of fluid

where is mass of small portion of fluid with volume

Incompressible fluid is a fluid which density remains constant for the fluid flow

Ideal fluid is a fluid flowing without friction

Continuity equation for incompressible fluid for any two sections 1 and 2

or for any section

Bernoulli equation for ideal fluid for any two points 1 and 2

or for any point

Measuring of stream speed with Pitot tube

Here:

 is density of liquid in the tube

 is density of fluid

h is height of liquid column in the tube

v is speed of fluid

Bernoulli equation for Pitot tube in ideal fluid

The relation between height of liquid column in the tube and the speed of fluid

Lift on wing

Where:

v is speed of the fluid relative to the wing

 is density of the fluid

L₁ and L₂ are lengths of bottom and top edges of the wing respectively

A is area of wing's plane

Bernoulli equation for wing in ideal fluid

The resultant upward pressure on the wing

The lift on the wing

Motion in viscous fluid

Here:

v(z) is velocity profile of the fluid relative to the plate as function of z-coordinate

A is area of the plate

Reynolds Number

where:

 is density of fluid

v is velocity of fluid

 is dynamic viscosity of fluid

L is length of object in the direction of motion

Laminar flow is flow of fluid without curls when its layers don't get mixed up. Here induvidual particles move along well defined paths and do not cross one another. For smooth surfaces this approximately takes place at

Re < 500

Turbulent flow is flow of fluid with curls when the layers get mixed up. Here ndividual particles move in a zig zag way by crossing one another. For smooth surfaces this approximately takes place at

Re > 2000

Transitional flow is intermediate flow between laminar and turbulent, taking place at

500 < Re < 2000

Friction force in viscous fluid for laminar flow

where:

 is dynamic viscosity of the fluid

 is z-component of velocity gradient