Bernoulli's equation and conservation of energy

In summary, the derivation of Bernoulli's equation using conservation of energy can be found in many sources. The equation equates the work done on a system to the change in kinetic and potential energy of the system. The blue volumes represent the same volume of fluid as it moves in time, while the rest of the fluid remains unchanged. This can be better understood by considering the entire chunk of fluid between the two cross-sections as "the system" and studying the effects of the pressure and movement on that system.
  • #1
broegger
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0
Can anyone explain to me how Bernoulli's equation arises from conservation of energy?
 
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  • #3
Why is it that you only account for the kinetic and potential energy change in the blue volumes.. What about the fluid between them?
 
  • #4
The blue volumes are assumed to be the same volume of fluid as it proceeds in time.

You're looking at two different time slices
 
  • #5
Originally posted by broegger
Why is it that you only account for the kinetic and potential energy change in the blue volumes.. What about the fluid between them?
All the action takes place in those end volumes. Nothing changes for the fluid between them.

Here's how to understand this derivation. Think of the entire chunk of fluid between the two cross-sections (A1 & A2) as "the system" to be studied. We want to study what happens when that system moves such that each end sweeps out a given volume of fluid. What Bernoulli's equation does is equate the work done on the system (done by the pressure at each end) to the change of kinetic and potential energy of the system.

To answer your question again, note that the net effect, as far as calculating the change in energy goes, is to move a mass of fluid from one end to the other. This is the only mass that changes kinetic and potential energy---the rest of the fluid doesn't change.

Make sense?
 

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and elevation of a fluid flowing through a pipe or tube. It states that the total energy of the fluid remains constant as it moves through different sections of the pipe, assuming there is no energy loss due to friction or other external factors.

2. How is Bernoulli's equation derived?

Bernoulli's equation can be derived from the principles of conservation of mass and conservation of energy. By applying these principles to a small volume of fluid traveling through a pipe, we can arrive at the equation that relates the pressure, velocity, and elevation of the fluid.

3. What is the significance of Bernoulli's equation?

Bernoulli's equation is significant because it allows us to make predictions about the behavior of fluids in different situations. It is used in various applications, such as in the design of airplanes, cars, and pipes for fluid transportation. It also helps us understand the relationship between pressure and velocity in a fluid, which is essential in many engineering and scientific fields.

4. How does Bernoulli's equation relate to conservation of energy?

Bernoulli's equation is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. In the case of a fluid, the energy is conserved as it moves through different sections of a pipe, with some energy being converted between potential and kinetic forms.

5. What are the limitations of Bernoulli's equation?

Bernoulli's equation assumes that the fluid is incompressible, inviscid (no internal friction), and flows along a streamline. It also does not account for energy losses due to factors such as turbulence and heat transfer. Therefore, it may not accurately predict the behavior of real fluids in all situations and should be used with caution.

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