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gamz95
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Bernoulli vs Energy Conservation?
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In summary, the conversation discusses the possibility of having the same velocities at the two ends of a tube, constructing an energy conservation equation, and the expectation of mechanical energy to be conserved in the presence of turbulence. The problem statement specifies a frictionless flow. The solution shows that the final equation is F=ma. However, there is a question about the physical possibility of having the same velocities and a changing velocity profile. The concept of transient 1D momentum equation is mentioned and the integration of it between the two ends of a control volume is discussed, which results in the ordinary Bernoulli terms and a term involving the rate of change of momentum.
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sophiecentaur
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Why would you expect mechanical energy to be conserved if there is any turbulence involved? Same velocities doesn't imply no energy loss.
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The problem statement does say "frictionless... flow."sophiecentaur said:
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It is shown right in the solution they gave. If you look at their final equation, it's just F = ma.gamz95 said:
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gamz95
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Yes it is indeed frictionless. Therefore, when normal energy equation constructed the KE1=KE2(Since it says that velocities are the same). However, how is this physically possible? And question gives a changing velocity profile(not a constant velocity).
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If you take the transient 1D momentum equation and integrate between the two ends of a control volume in which the velocity within the control volume is changing with time (and possibly position), you get the ordinary Bernoulli terms plus a term involving the rate of change of momentum with time within the control volume. See the PDF at Unsteady Bernoulli Equation - MIT OpenCourseWare that can be reached by googling transient Bernoulli equation.gamz95 said:
1. What is the difference between Bernoulli's equation and the principle of energy conservation?
Bernoulli's equation is a mathematical relationship that describes the conservation of energy in a fluid flow system. It relates the pressure, velocity, and height of a fluid at different points in the system. On the other hand, the principle of energy conservation states that energy cannot be created or destroyed, only transferred or transformed. It applies to all systems, not just fluid flow.
2. Can you use Bernoulli's equation and the principle of energy conservation interchangeably?
No, they are not interchangeable. While both concepts involve the conservation of energy, Bernoulli's equation is specific to fluid flow systems and cannot be applied to other systems. The principle of energy conservation, on the other hand, can be applied to all types of systems.
3. How does Bernoulli's equation demonstrate energy conservation?
Bernoulli's equation is based on the principle of energy conservation. It shows how the total energy of a fluid flowing through a system remains constant, even as it changes forms between kinetic energy, potential energy, and pressure energy. This demonstrates the conservation of energy within the fluid flow system.
4. Which one is more accurate: Bernoulli's equation or the principle of energy conservation?
Both Bernoulli's equation and the principle of energy conservation are accurate in their own right. Bernoulli's equation is a simplified version of the more general principle of energy conservation, and it is accurate as long as certain assumptions are met, such as steady flow and incompressible fluids. The principle of energy conservation, however, is a universal law and is always accurate.
5. Is energy always conserved in a fluid flow system according to Bernoulli's equation?
In ideal conditions, energy is always conserved in a fluid flow system according to Bernoulli's equation. However, in real-world situations, there may be some energy losses due to factors such as friction and turbulence. In these cases, Bernoulli's equation may not fully account for all energy changes, and the principle of energy conservation should be used to analyze the system.
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