what exactly does Bernouilli's principle mean?

Question

well, i know it states that as the velocity of a fluid increases, its pressure decreases and vice versa. but for example if i squeeze the end of a hose with running water, pressure is increased (due to the reduced diameter) and hence you see the water flowing out at greater velocity which seems to contradict the principle.

Answer 1

In non viscous fluid mechanics, there are essetially two principle in play : 1. the Principle of Continuity 2. The Bernoulli's Principle

The former states that the rate of flow of liquid is same throughout the length of a pipe etc. i.e A1 * V1 = A2 * V2 ( where A and V are the Area of Cross section and Velocity of liquid at different stages)
Thus, when u squeeze the hose the A decreases and to maintain the equation the V has to increase.

The Bernoulli's Principle relates the Energies of two different stages :
P1 + 1/2 p*V1*V1 + p*g*H1 = P2 + 1/2 p*V2*V2 + p*g*H2

Where P,p,H are the Pressure, density and Height.

SURPRISINGLY, using the above eqn, we find that when we squeeze the hose, the PRESSURE actually decreases rather than what we think logically.

Answer 2

You are equating two things that do not relate in the way you are assuming.

The distance the water goes when it leaves the end of the pipe depends on its velocity at the nozzle, and has nothing to do with its pressure.

If the mains supply is sufficiently good, the pressure at the nozzle will not change as you restrict it. But the flow rate will go up, so the pressure of the water beyond the nozzle will fall. This is down to the change in resistance.

To see this more clearly, imagin squeezing the nozzle more and more and more until its just a dribble coming out. Now by your thinking the pressure is as high as you can make it, but the hose just drips - the drips should be flying across the garden!

Answer 3

The hose pipe is a different thing:

When the end is squeezed the *flow rate* along the pipe is reduced. It is fundamental to thermodynamics that this reduces *losses* in the pipe - the amount of work energy dissipated into heat energy. So there is a reduced *head loss*, loss of pressure, for the water flowing through the pipe. Hence the water spurts higher.

Bernoulli's law is not talking about losses it's a statement about the conservation of energy in fluids.

Answer 4

While the situation you described seems to contradict the principle it does not. You see, if a fluid is moving in a horizontal direction and encounters a pressure difference, it will result in a net force, which by Newton's 2nd law (which states in the presence of an outside force there will be acceleration) will cause an acceleration of the fluid. Work (the product of force and distance) is equal to a change in kinetic energy (energy of motion). In this situation it can be expressed as (change in pressure) x volume = (change in kinetic energy). This could be written as (change in pressure) + (change in kinetic energy)/volume = 0. In other words: (change in pressure) + (change in kinetic energy)/volume = constant, which is indeed Bernouilli's principle. Since kinetic energy is written as 1/2mv^2, the amount of water coming out of the hose is less, therefore less mass, so it is possible for the principle to hold true in this situation.

Answer 5

Acording to Bernouilli 's principle the net energy contained by a liquid is constant . It is just eqwuivalent to energy conservation principle. When you press the pipe the pressure of the liquid applied on the walls of pipe decreases (since you have compressed it by your hand) so to conserve energy velocity of water rises i.e Kinetic energy increases

Answer 6

Bernoulli's principle actually represents principle of conservation of energy. It ultimately states that the total energy ( which is the some of pressure head ,velocity head and potential head) of a liquid always remain constant. In the case you described above ,on pressing the pipe actually velocity head increases not the pressure head.

Answer 7

well u r correct but 4 more details i wud like u to consult the NCERT BOOK OF CLASS 11th Page no. 231.The chapter name is Mechanics and Fluids.or u can look up in an encyclopedia 4 that or can consult any refresher book.
And even if u r not satisfied then u must go n talk to a teacher who teaches classe 11th and 12th.It will b the best option 4 u.

Answer 8

http://home.earthlink.net/~mmc1919/venturi.html