MadSci Network: Physics Query:

### Re: Bernoulli questions

Date: Mon Jul 9 11:13:17 2001
Posted By: Jaime Valencia-Rodríguez, Guest Researcher, Chemical Science and Technology Lab, NIST.
Area of science: Physics
ID: 993910247.Ph
Message:
```
Dear Ravi:

Thank you very much for your question.
Bernoulli's principle is a very interesting topic.

Let us consider first what the following site says:
http://www.britannica.
com/eb/article?eu=80998

Bernoulli's theorem: in fluid dynamics, relation among the pressure,
velocity, and elevation in a moving fluid (liquid or gas), the
compressibility and viscosity (internal friction) of which are negligible
and the flow of which is steady, or laminar. First derived (1738) by the
Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that
the total mechanical energy of the flowing fluid, comprising the energy
associated with fluid pressure, the gravitational potential energy of
elevation, and the kinetic energy of fluid motion, remains constant.
Bernoulli's theorem is the principle of energy conservation for ideal
fluids in steady, or streamline, flow.
Bernoulli's theorem implies, therefore, that if the fluid flows
horizontally so that no change in gravitational potential energy occurs,
then a decrease in fluid pressure is associated with an increase in fluid
velocity. If the fluid is flowing through a horizontal pipe of varying
cross-sectional area, for example, the fluid speeds up in constricted
areas
so that the pressure the fluid exerts is least where the cross section is
smallest. This phenomenon is sometimes called the Venturi effect, after
the
Italian scientist G.B. Venturi (1746-1822), who first noted the effects of
constricted channels on fluid flow.
Bernoulli's theorem is the basis for many engineering applications, such
as
aircraft-wing design. The air  flowing over the upper curved surface of an
aircraft wing moves faster than the air beneath the wing, so that the
pressure underneath is greater than that on the top of the wing, causing
lift.

Please note that Bernoulli's theorem asks for frictionless motion. Of
course this is not the case in the ocean floor, fore example. In this case
the fluid is flowing in a turbulent fashion and this causes the apparition
of vortices and some other complex motions, because the liquid in contact
with the floor will travel at a smaller velocity than the liquid which is
just above this first layer.

Now, in the following link:
http://ldaps.ivv.na
sa.gov/Physics/bernoulli.html

we find:

Bernoulli's Theorem
How pressure and velocity interact
static pressure + dynamic pressure = total pressure = constant
static pressure + 1/2 x density x velocity2 = total pressure = constant

General Concept:
The Bernoulli effect is simply a result of the conservation of energy. The
work done on a fluid (a fluid is a liquid or a gas), the pressure times
the
volume, is equal to the change in kinetic energy of the fluid.

General Facts:
Where there is slow flow in a fluid, you will find increased pressure.
Where there is increased flow in a fluid, you will find decreased
pressure.

In a real flow, friction plays a large role - a lot of times you must have
a large pressure drop (decrease in pressure) just to overcome friction.
This is the case in your house. Most water pipes have small diameters
(large friction), hence the need for "water pressure" - it is the energy
from that pressure drop that goes to friction.

A showerhead (if you have a fancy one) has a number of different operation
modes. If you go for the "massage" mode, you are moving a little water
fast. For the "lite shower," you are moving a lot of water slowly. It
takes
the same amount of energy to move a little water fast as it does to move a
lot of water slowly. This is the amount of energy you have due to your
"water pressure".
http://ldaps.ivv.nasa.gov/Physics/Images/Engineering_Manual4.gif

Some practical problems are considered in the very interesting link:

http://www.saj.fi/saj-
bernoulli.htm

A section I want to highlight says:

In a real flow i.e. around an immersed body, friction plays a large role -
most of the time when the ship is in service you have a large pressure
drop
(decrease in pressure) just to overcome friction. For example, if you have
a water pipe with a small diameter (large friction), hence the need for
"water pressure" - it is the energy from that pressure drop that goes to
friction.

Example

When a liquid runs freely through a pipe of a constant area (B), to which
three ascension pipes (D,E,F) are connected, the static pressure will
decrease along the dashed line towards the outlet (Fig.1), The pressure
decreases as result of friction loss in the horizontal pipe.
http://www.saj.fi/images/Pipeflow1.gif

Fig. 1

In (Fig.2) the area has been changed in two places, with a thinner pipe at
section (G) and a thicker pipe at section (H). The following occurs:

Section (G)

The resultant constriction causes the liquid to move at a higher speed,
increasing the dynamic pressure, with the result that the static pressure
in pipe (D) falls below the dashed line.

Section (H)

In section (H), which has a much larger area, the static pressure rises
above the dashed line, the speed of the liquid having decreased due to the
larger area, with the result that the dynamic pressure will be decreased.
http://www.saj.fi/images/Pipeflow2.gif

Fig. 2

A more somewhat more technical discussion could be found in:

http://physics.bu.e
du/py105/notes/Bernoulli.html

I hope this helps

Regards

Jaime Valencia

```

Current Queue | Current Queue for Physics | Physics archives