MadSci Network: Physics

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

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:

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 
so that the pressure the fluid exerts is least where the cross section is 
smallest. This phenomenon is sometimes called the Venturi effect, after 
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 
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 

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:

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 
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 

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.

Example: the showerhead
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 
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".


Some practical problems are considered in the very interesting link:

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 
(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 


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.

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.
Fig. 2

A more somewhat more technical discussion could be found in:


I hope this helps


Jaime Valencia

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