Ever thought of How can a plane fly?
In a
storm how does a house lose its roof?
Why do rabbits not suffocate in the burrows?
Why does a cricket ball swing or a baseball
curve?
Here the answer is given by the bernoulli’s
principle !
Bernoulli’s Equation:
Let us focus our attention on the motion of the shaded
region. This its our “system”. The lower cylindrical element of fluid of length, A1 is at height y1 which moves with speed v1After some
time, the leading section of our system fills the upper cylinder of fluid of
length and area
A2 at
height y2,
and is then moving with speed v2.
A pressure force F1 acts on the lower part
of the cylindrical tube towards right and pressure force F2 acts on the upper part of the cylindrical tube
towards left. The net work done on the system F1 and F2 is
Where we have used the relations and. The net effect of the motion of the system is
to raise the height of the lower cylinder of mass and to change its speed. The changes in the
potential and kinetic energies are
Since the density is, we have .
Since the points 1 and 2 can be chosen arbitrarily, we can express this
result as Bernoulli’s Equation = constant
It is applied to all points along a streamline in a nonviscous,
incompressible and irrotational fluid.
In a
storm how does a house lose its roof?
Air flow is disturbed by the house. The
"streamlines" crowd around the top of the roof.
⇒faster flow above house
⇒reduced pressure above
roof to that inside the house
⇒roof lifted off because
of pressure difference.
Why do
rabbits not suffocate in the burrows?
Air
must circulate. The burrows must have two entrances. Air flows across the two
holes is usually slightly different
⇒ slight pressure
difference
⇒ forces flow of air
through burrow.
One
hole is usually higher than the other and the a small mound is built around the
holes to increase the pressure difference.