Bernoulli's Principle Problem/Energy Conservation

In summary, the problem involves water flowing through a sprinkler system with a level hose connected to a nozzle directed upwards. The water exits the nozzle and reaches a height h before falling back into a pool. The hose is connected to a reservoir with a pressure Pres, and the problem asks for the best expressions for the velocity of the water just after it leaves the nozzle and the height h. Using Bernoulli's equation and conservation of energy, the correct expression for the velocity is Vexit = (2[(Pres-Patm)/ρ])^(1/2), and the correct expression for the height is h = Vexit^2/2g. The confusion about the ρgh term is due to the fact that the problem does
  • #1
erinfalk
1
0

Homework Statement


Hi! The problem states: Water through a certain sprinkler system flows trhough a level hose connected to a nozzle which is directed directly upwards. The water leaves the nozzle and shoots to a height, h, before falling back down again into a pool.
The hose is connected to a reservoir which maintains the water there at a pressure, Pres Assume no viscosity of flow, until water exits the nozzle. Use the following notation:
Anoz= cross sectional area of nozzle
Lhose=length of hose
Patm=atmospheric pressure
ρ=density of water

What is the best expression for the velocity of the water just after it leaves the nozzle? (A)
What is the best expression for the height, h? (B)



Homework Equations


Bernoulli's equation, and conservation of energy (Initial kinetic energy of water=final potential energy of water at height, h)


The Attempt at a Solution



So, I actually was fine on the calculation of this problem, but I am having difficulty understanding the rationale behind (A). I calculated Vexit= (2[(Pres-Patm)/ρ])^(1/2)
However, to do this, I ignored the velocity of the water in the reservoir. That makes sense, it is hardly moving compared to the velocity of the novel because the regions have equal flow rates. However, I also ignored the ρgh term for the water in the reservior. I guess that I am confused as to why this term doesn't have to be taken into account.

If anyone could explain, that would be great!

 
Physics news on Phys.org
  • #2
erinfalk said:

Homework Statement


Hi! The problem states: Water through a certain sprinkler system flows trhough a level hose connected to a nozzle which is directed directly upwards. The water leaves the nozzle and shoots to a height, h, before falling back down again into a pool.
The hose is connected to a reservoir which maintains the water there at a pressure, Pres Assume no viscosity of flow, until water exits the nozzle. Use the following notation:
Anoz= cross sectional area of nozzle
Lhose=length of hose
Patm=atmospheric pressure
ρ=density of water

What is the best expression for the velocity of the water just after it leaves the nozzle? (A)
What is the best expression for the height, h? (B)



Homework Equations


Bernoulli's equation, and conservation of energy (Initial kinetic energy of water=final potential energy of water at height, h)


The Attempt at a Solution



So, I actually was fine on the calculation of this problem, but I am having difficulty understanding the rationale behind (A). I calculated Vexit= (2[(Pres-Patm)/ρ])^(1/2)
However, to do this, I ignored the velocity of the water in the reservoir. That makes sense, it is hardly moving compared to the velocity of the novel because the regions have equal flow rates. However, I also ignored the ρgh term for the water in the reservior. I guess that I am confused as to why this term doesn't have to be taken into account.

If anyone could explain, that would be great!

Can you draw the diagram of the problem please ? Looks like you are confused with wordings.
 
  • #3
erinfalk said:
However, I also ignored the ρgh term for the water in the reservior. I guess that I am confused as to why this term doesn't have to be taken into account.

If anyone could explain, that would be great!

Homework Statement





You were given the pressure in the reservoir at the point where the hose connects to it. So there is no change in potential energyfrom that point until the water squirts out of the nozzle & climbs.

Had the problem stated 'the hose is connected to a point h below the surface of the water', then you would have had to use p = patm + rho g h. The result would have been the same.

The problem statement did not make clear whether pres included patm. You might want to check on that.
 

1. What is Bernoulli's Principle?

Bernoulli's Principle is a physical law that states that as the speed of a fluid (such as air or water) increases, its pressure decreases. This principle is used to explain various phenomena in fluid dynamics, such as lift in airplane wings or the flow of water through pipes.

2. How does Bernoulli's Principle relate to energy conservation?

Bernoulli's Principle is directly related to the conservation of energy because it shows that the total energy of a fluid (kinetic energy + potential energy) remains constant as the fluid moves through different regions of varying pressure. This is known as the Bernoulli's equation, which mathematically represents the conservation of energy in a fluid system.

3. Can you provide an example of Bernoulli's Principle in action?

One common example of Bernoulli's Principle is the lift force generated by airplane wings. As air moves over the curved surface of an airplane wing, its speed increases and pressure decreases, creating a region of lower pressure above the wing. This difference in pressure creates a net upward force, lifting the airplane off the ground.

4. What are some practical applications of Bernoulli's Principle?

Bernoulli's Principle has a wide range of practical applications, including in the design of airplane wings, wind turbines, and carburetors. It is also used in the study of weather patterns, ocean currents, and blood flow in the human body.

5. Are there any limitations to Bernoulli's Principle?

Bernoulli's Principle is a simplified model that does not account for factors such as viscosity, turbulence, and compressibility of fluids. In certain cases, these factors may significantly affect the accuracy of calculations based on Bernoulli's Principle. Additionally, the principle only applies to incompressible fluids, meaning that it cannot be used to explain the behavior of gases.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
837
Replies
204
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
16
Views
2K
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
560
Back
Top