Bernoulli's Principle
It states that as the speed of a moving
fluid (liquid or gas) increases, the pressure within the fluid
decreases. The phenomenon described by Bernoulli's principle has many
practical applications. Bernoulli's principle thus says that a rise
(fall) in pressure in a flowing fluid must always be accompanied by a
decrease (increase) in the speed, and conversely, if an increase
(decrease) in , the speed of the fluid results in a decrease (increase)
in the pressure.
Bernoulli's principle can be explained in terms of the
law of conservation of energy. As a fluid moves from a wider pipe into a
narrower pipe or a constriction, a corresponding volume must move a
greater distance forward in the narrower pipe and thus have a greater
speed. At the same time, the work done by corresponding volumes in the
wider and narrower pipes will be expressed by the product of the
pressure and the volume. Since the speed is greater in the narrower
pipe, the kinetic energy of that volume is greater. Then, by the law of
conservation of energy, this increase in kinetic energy must be balanced
by a decrease in the pressure-volume product, or, since the volumes are
equal, by a decrease in pressure.
Bernoulli’s principle can be derived from the principle of conservation of energy. This states that in a steady flow the sum of all forms of mechanical energy in a fluid along a restructure is the same at all points on that simplify:
½ mv2 + mgh + pv = constant ............1
However, the above equation is not useful in fluid mechanics, as it is not clear what is meant by the velocity of the fluid of mass m - the velocity changes in any small volume of fluid. Thus, we divide the above equation by V to obtain the energy content of an arbitrarily small volume:
Rho x v2 + rho x g x h + p = constant...............2
Rho x v2 + rho x g x h + p = constant...............2
Let us consider two points on a streamline (the path of a fluid particle), denoted by 1 and 2, the flow is from 1 to 2. Than, if the fluid is ideal (no friction and incompressible) and the flow is steady, we have
P1 + rho/2 (v1)2 + rho x g x h1 = P2 + rho/2 (v2)2 + rho x g x h2
Bernoulli's principle is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton's 2nd law will cause an acceleration of the fluid. The fundamental relation,
Work done = Change in Kinetic Energy (KE)
This equation can be written as
- (Change in Pressure) x Area x Distance = Change in Kinetic Energy (KE)
This furthermore can be expressed as
P1 + rho/2 (v1)2 + rho x g x h1 = P2 + rho/2 (v2)2 + rho x g x h2
Bernoulli's principle is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton's 2nd law will cause an acceleration of the fluid. The fundamental relation,
Work done = Change in Kinetic Energy (KE)
This equation can be written as
- (Change in Pressure) x Area x Distance = Change in Kinetic Energy (KE)
This furthermore can be expressed as
(Change in Pressure) + Change in (Kinetic Energy / Volume) = 0
i.e.…
Pressure + (Kinetic Energy / Volume) = Constant (C)
This is known as Bernoulli’s principle. This is at the heart of a number of everyday phenomena. As a very trivial example, A useful example is provided by the functioning of a perfume bottle: squeezing the bulb over the fluid creates a low pressure area due to the higher speed of the air, which subsequently draws the fluid up.
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 who first noted the effects of constricted channels on fluid flow.
i.e.…
Pressure + (Kinetic Energy / Volume) = Constant (C)
This is known as Bernoulli’s principle. This is at the heart of a number of everyday phenomena. As a very trivial example, A useful example is provided by the functioning of a perfume bottle: squeezing the bulb over the fluid creates a low pressure area due to the higher speed of the air, which subsequently draws the fluid up.
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 who first noted the effects of constricted channels on fluid flow.