# Fluids: Bernoulli's Equation Derivation Question

• I
• Sbee
In summary, the pressure force exerted on the wider section of the fluid is greater than the pressure force exerted on the narrower section because something is slowing the emerging fluid.

#### Sbee

TL;DR Summary
Hi,
Studying Bernoulli's equation derivation and am not understanding WHY is the second Force for the larger distance applied in the direction OPPOSITE to the flow of the velocity?

I am using this textbook figure:
https://openstax.org/books/university-physics-volume-1/pages/14-6-bernoullis-equation

The derivation starts at "We also assume that there are no viscous forces in the fluid, so the energy of any part of the fluid will be conserved. "
I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure.
Thanks!

Delta2
Sbee said:
Summary:: Hi,
Studying Bernoulli's equation derivation and am not understanding WHY is the second Force for the larger distance applied in the direction OPPOSITE to the flow of the velocity?

I am using this textbook figure:
https://openstax.org/books/university-physics-volume-1/pages/14-6-bernoullis-equation

The derivation starts at "We also assume that there are no viscous forces in the fluid, so the energy of any part of the fluid will be conserved. "

I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure.
Thanks!
What direction do you think the pressure force exerted on the portion of the fluid under consideration by the fluid ahead of it should be acting?

F2 means the outlet pressure of the system converted to energy

horacio torres said:
F2 means the outlet pressure of the system converted to energy
What does this mean? How can pressure be converted to energy? How does it relate to the direction of F2?

Chestermiller said:
What direction do you think the pressure force exerted on the portion of the fluid under consideration by the fluid ahead of it should be acting?
It should be acting to the right, because the pressure is coming from the left side of the fluid and because the velocity is to the right!

Sbee said:
It should be acting to the right, because the pressure is coming from the left side of the fluid and because the velocity is to the right!
You're looking at the forces exerted by the surrounding materials on the fluid in the picture. Does pressure exert a pushing force or a pulling force? When you do a force balance on a body, do you include the forces it exerts on surrounding bodies, or only the forces the they exert on it?

Sbee and sophiecentaur
Sbee said:
It should be acting to the right, because the pressure is coming from the left side of the fluid and because the velocity is to the right!
Think about Newton's 2nd Law. If the gas is traveling slower, which direction must the force be acting, to make this happen? (It may not feel right, intuitively but Newton tells you what really happens.)

Sbee and Chestermiller
sophiecentaur said:
Think about Newton's 2nd Law. If the gas is traveling slower, which direction must the force be acting, to make this happen? (It may not feel right, intuitively but Newton tells you what really happens.)
I was thinking about Newton's 3rd law. The fluid in the control volume exerts a force of magnitude F2 on the fluid ahead of it, and the fluid ahead of it exerts an equal and opposite force of magnitude F2 on the fluid in the control volume. The latter is the force shown in the OP's diagram.

Chestermiller said:
I was thinking about Newton's 3rd law. The fluid in the control volume exerts a force of magnitude F2 on the fluid ahead of it, and the fluid ahead of it exerts an equal and opposite force of magnitude F2 on the fluid in the control volume. The latter is the force shown in the OP's diagram.
The directions of arrows is always difficult but if we follow the sums, the answer comes out either way. My way of explaining the increase in pressure in the wide section is that ‘something’ must be slowing the emerging fluid. Hence the direction of that something, in my head.

sophiecentaur said:
The directions of arrows is always difficult but if we follow the sums, the answer comes out either way. My way of explaining the increase in pressure in the wide section is that ‘something’ must be slowing the emerging fluid. Hence the direction of that something, in my head.
I was just thinking that, when we do a free body diagram force balance on a body, we only show the forces that other bodies exert on it, not the forces that it exerts on other bodies.

sophiecentaur
I'm not sure, I think I have to move on but if I understand it later I'll let you know

Sbee said:
I'm not sure, I think I have to move on but if I understand it later I'll let you know
Good luck.

sophiecentaur

## 1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental principle in fluid dynamics that describes the relationship between fluid pressure, velocity, and elevation. It states that as the speed of a fluid increases, its pressure decreases, and vice versa.

## 2. How is Bernoulli's equation derived?

Bernoulli's equation can be derived from the principle of conservation of energy, which states that the total energy in a system remains constant. By considering the different forms of energy in a fluid system (kinetic, potential, and pressure), we can derive the equation.

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

Bernoulli's equation is significant because it helps us understand and predict the behavior of fluids in various situations. It is used in many engineering applications, such as designing airplanes and calculating water flow in pipes.

## 4. What are the assumptions made in Bernoulli's equation?

The assumptions made in Bernoulli's equation include the fluid being incompressible, non-viscous, and steady flow. It also assumes that the fluid is flowing along a streamline, and there are no external forces acting on the fluid.

## 5. Can Bernoulli's equation be applied to all fluid systems?

No, Bernoulli's equation is only applicable to certain types of fluid systems, such as incompressible fluids with steady flow. It cannot be applied to systems with compressible fluids, turbulent flow, or external forces acting on the fluid.