Application of Bernoulli’s Equation to Fluid Dynamics
Bernoulli’s equation has been used widely in an engineering aspects, the conservation of energy is the most famous one. This paper will talk about the application of Bernoulli’s equation to fluid dynamics. Fluids flow can be in different forms, such as water in the ocean, blood within our body and etc. Thus, it is necessary to study the mechanism of fluids.
In the year of 1738, Daniel Bernoulli published a book called Hydrodynamica, which introduces a principle that has a great impact on fluid dynamics. The principle then is named after him, called Bernoulli principle. This principle implies that there will be a decrease in pressure if the speed of the fluid flow increases[1]. This principle …show more content…
1. Schematic illustration of choosing two points in the fluid. (Adapted from NASA: http://www.grc.nasa.gov/WWW/k-12/airplane/bern.html )
The Bernoulli’s equation can be derived from the conservation of energy: work done = kinetic energy + potential energy, which can be expressed as ∆W= ∆K+ ∆U and with the help of Newton’s second law. The kinetic energy can be written as K= 1/2 mv^2 and the potential energy can be written as U= mgh . By plugging terms for different points and rearranging the terms, we can derive the Bernoulli’s equation without too much effort. The details of the derivation can be found somewhere else.
The Bernoulli’s principle can be derived from the Bernoulli’s equation by assuming no changes made to the height of the fluid flow, which can be rewritten as 〖 P〗_1+ 1/2 ρv_1^2= P_2+ 1/2 ρv_2^2 (2) or 〖 P〗_1+ 1/2 ρv_1^2= constant (3)
By looking at equation (3), we can interpret the Bernoulli’s principle as such: if the speed of the fluid increases, the pressure of the fluid will be dropped to keep the equation constant, which is coincident to the Bernoulli’s
Bernoulli’s equation has been used widely in an engineering aspects, the conservation of energy is the most famous one. This paper will talk about the application of Bernoulli’s equation to fluid dynamics. Fluids flow can be in different forms, such as water in the ocean, blood within our body and etc. Thus, it is necessary to study the mechanism of fluids.
In the year of 1738, Daniel Bernoulli published a book called Hydrodynamica, which introduces a principle that has a great impact on fluid dynamics. The principle then is named after him, called Bernoulli principle. This principle implies that there will be a decrease in pressure if the speed of the fluid flow increases[1]. This principle …show more content…
1. Schematic illustration of choosing two points in the fluid. (Adapted from NASA: http://www.grc.nasa.gov/WWW/k-12/airplane/bern.html )
The Bernoulli’s equation can be derived from the conservation of energy: work done = kinetic energy + potential energy, which can be expressed as ∆W= ∆K+ ∆U and with the help of Newton’s second law. The kinetic energy can be written as K= 1/2 mv^2 and the potential energy can be written as U= mgh . By plugging terms for different points and rearranging the terms, we can derive the Bernoulli’s equation without too much effort. The details of the derivation can be found somewhere else.
The Bernoulli’s principle can be derived from the Bernoulli’s equation by assuming no changes made to the height of the fluid flow, which can be rewritten as 〖 P〗_1+ 1/2 ρv_1^2= P_2+ 1/2 ρv_2^2 (2) or 〖 P〗_1+ 1/2 ρv_1^2= constant (3)
By looking at equation (3), we can interpret the Bernoulli’s principle as such: if the speed of the fluid increases, the pressure of the fluid will be dropped to keep the equation constant, which is coincident to the Bernoulli’s