The Help With Assignment Blog is intended to provide with tips and tricks to students so that they are able to do better at school and college. The Blog is associated with HelpWithAssignment.com (HwA), a leading provider of online tuitions in University subjects.

## Monday, July 11, 2011

### Bernoulli’s Theorem in Chemical Engineering from HelpWithAssignment.com

Bernoulli’s Theorem in Chemical Engineering

Bernoulli’s Theorem in fluid dynamics is one of the important discoveries. The relation among pressure, velocity and elevation in a moving fluid, the compressibility and viscosity of which are negligible and the flow of which is steady or laminar. The Theorem was first derived in 1738 by Swiss mathematician Daniel Bernoulli. The theorem states that, 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 principle can be applied to various types of fluid flow. There are different applications of Bernoulli’s Theorem. The theorem can be derived through the law of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy and a decrease in its static pressure and potential energy. If the fluid is flowing out of a reservoir the sum of all forms of energy is the same on all the streamlines because in a reservoir the energy per unit mass is the same everywhere.

Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can occur only because the fluid on that section has moved from a region of a higher pressure to a region of lower pressure and it its speed decreases, it can only occur because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.

In most liquid flows and gas flows at high speeds, the mass density of a fluid parcel can be considered to be constant, regardless, of pressure variations in the flow. For this reason the fluid in such flows can be considered to be incompressible and these flows can be described as incompressible flow. Bernoulli performed experiments on liquids and his equation in its original form is valid only in incompressible flow. A common form of Bernoulli’s equation, valid at any arbitrary point along a streamline where gravity is constant, is:

V2/2 + gz + p/ρ = constant

Where,

v is the fluid flow speed at a point on a streamline

g is the acceleration due to gravity

z is the elevation of the point above a reference plane, with the positive z-direction pointing upward – so in the direction opposite to the gravitational acceleration

p is the pressure of the fluid at all the points in the fluid

ρ is the density of the fluid at all points in the fluid

For conservative force fields, Bernoulli’s equation can be generalized as

V2/2 + Ψ + p/ρ = constant

Where, Ψ is the force potential at the point considered on the streamline.

For more details you can visit our website at http://www.helpwithassignment.com/chemical-engineering-assignment-help and http://www.helpwiththesis.com

#### 1 comment:

Anonymous said...

brinkka2011 says: I was very happy to seek out this net-site. I wished to thank in your time for this glorious read! I definitely enjoying each little bit of it. Can I simply say what a reduction to find someone who actually is aware of what they are talking about on the internet. It's laborious to search out knowledgeable individuals on this subject however you definitely know easy methods to convey an issue to light and make it important. Extra folks have to read this and perceive this facet of the story. I cant believe youre not more standard since you undoubtedly have the gift. however you sound like you understand what you're speaking about. Additionally, I simply gave this onto a colleague who was doing a little analysis on this. And he reality is bought me breakfast outcome I discovered it for him. So let me reword that: Thanks for the deal with and for spending the time to debate this, I really feel strongly about it and love studying extra on this topic. If attainable, would you mind updating your weblog with more particulars? Its highly helpful for me. Big thumb up for this blog submit!