Bernoulli's equation derivation

In summary, the work energy theorem states that the change in kinetic energy is equal to the work of all forces. In the case of a conservative force, the work done is equal to the negative change in potential energy. This explains the use of the work energy theorem in Bernoulli's equation derivation, where one force comes from pressure and the other from gravity.
  • #1
logearav
338
0

Homework Statement



In bernoulli's equation derivation, we use Work energy theorem, in which work done is taken as change in kinetic energy plus change in potential energy.
But in mechanics, i have studied, Work energy theorem is simply change in kinetic energy.
So, which is correct? Pls help revered members

Homework Equations





The Attempt at a Solution


 
Physics news on Phys.org
  • #2
The work Energy Theorem states that the change of KE is equal to the work of all forces. If one of the forces is conservative, the work of that force is equal to the negative potential energy change. If you have two forces, Fa and Fb, and Fb is conservative, with PE(b) potential energy,

ΔKE=W(a)+W(b)=W(a) -ΔPE(b), that is W(a)= ΔKE+ΔPE(b)

When deriving Bernoulli's equation, one force comes from the pressure at the cross-sections of the tube containing the fluid. The other force is gravity.

ehild
 
  • #3
Thanks Mr.ehild for your beautiful explanation.
 

Related to Bernoulli's equation derivation

What is Bernoulli's equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between the pressure, velocity, and height of a fluid moving in a closed system.

What is the derivation of Bernoulli's equation?

The derivation of Bernoulli's equation involves applying the principles of conservation of mass and energy to a fluid element in motion, and simplifying the resulting equations to obtain the final form of the equation.

What assumptions are made in the derivation of Bernoulli's equation?

The derivation of Bernoulli's equation assumes that the fluid is incompressible, inviscid, and steady, and that the flow is irrotational and in the absence of external forces such as gravity.

What is the significance of Bernoulli's equation in fluid dynamics?

Bernoulli's equation is significant in fluid dynamics as it provides a simple and useful tool for analyzing and predicting the behavior of fluids in various applications, such as in pipes, pumps, and airplanes.

Can Bernoulli's equation be applied to all types of fluids?

No, Bernoulli's equation is only applicable to ideal fluids, which are fluids that do not experience viscosity or frictional forces. Real fluids, such as air and water, do not strictly follow Bernoulli's equation but can be approximated under certain conditions.

Similar threads

  • Introductory Physics Homework Help
2
Replies
61
Views
3K
Replies
207
Views
4K
  • Classical Physics
Replies
21
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
319
  • Introductory Physics Homework Help
Replies
10
Views
288
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
18
Views
3K
Replies
20
Views
2K
  • Introductory Physics Homework Help
2
Replies
56
Views
2K
Back
Top