How does a plane fly?
How does a perfume spray work?
Why does a cricket ball curve?
Derivation and Applications of the Bernoulli Principal
Grade 11 Physics
1.To apply Bernoulliís equation to solve problems
2.To describe Bernoulliís principle and to derive his formula in terms of conservation of energy
3.To present applications of the Bernoulli principle
As the speed of a fluid goes up, its pressure goes down!
The pressure in a fast moving stream of fluid is less than the pressure in a slower stream
Fast stream = low air pressure
Slow stream = High air pressure
ďfor any point along a flow tube or streamlineĒ
P + ½ v2 + g h = constant
Each term has the dimensions of energy / volume or energy density.
½ v 2 KE of bulk motion of fluid
g h GPE for location of fluid
P pressure energy density arising from internal forces within
moving fluid (similar to energy stored in a spring)
Transformation of SI Units to Joule/meter3= energy/volume:
P [Pa] = [N m-2] = [N m m-3] = [J m-3]
½ v2 [kg m-3 m2 s-2] = [kg m-1 s-2] = [N m m-3] = [J m-3]
g h [kg m-3 m s-2 m] = [kg m s-2 m m-3] = [N m m-3] = [J m-3]
For steady flow, the velocity, pressure, and elevation of an incompressible and nonviscous fluid are related by an equation discovered by Daniel Bernoulli (1700Ė1782).
Deriving Bernoulliís equation as Conservation of Energy
In a moving fluid p+½rV2 = constant everywhere