Fluid Mechanics
SI units & Physics constants
Fluid mechanics investigates motion of objects in fluid media
Here (all units see here):
A_{1} and A_{2} are cross section areas of tube at sections 1 and 2 respectively
v_{1} and v_{2} are velocities of fluid at sections 1 and 2 respectively
P_{1} and P_{2} are static pressures at sections 1 and 2 respectively
h_{1} and h_{2} 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
L_{1} and L_{2} 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 zcoordinate
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 zcomponent of velocity gradient
