Need Help Applying Bernoulli's Equation to a Fluid Mech Problem

In summary: If i plugin the values in my equation, i get the correct answer, thanks for the help Basic_Physics! :smile:
  • #1
Saitama
4,243
93

Homework Statement


http://i50.tinypic.com/2m2tbaq.png

Homework Equations


The Attempt at a Solution


I suppose i have to apply the Bernoulli's equation here but i don't even have the slightest idea on how to apply it here. I am a dumb at fluid mechanics, any help would be appreciated.
 
Physics news on Phys.org
  • #2
To solve for the velocity of flow you set Bernouli's equation up at the surface of the liquid and at the bottom of the opening. The pressure at both ends are atmospheric. The only point difficult to grasp is that the flow velocity at the surface is assumed to be zero, that is we assume that the container is very large and that the level is not dropping so that the water just beyond the entry point do not need to rush into the pipe due to the large source of water (this portion just outside of the top end of the pipe is still part of the streamlines).
 
  • #3
Basic_Physics said:
To solve for the velocity of flow you set Bernouli's equation up at the surface of the liquid and at the bottom of the opening. The pressure at both ends are atmospheric. The only point difficult to grasp is that the flow velocity at the surface is assumed to be zero, that is we assume that the container is very large and that the level is not dropping so that the water just beyond the entry point do not need to rush into the pipe due to the large source of water (this portion just outside of the top end of the pipe is still part of the streamlines).

If i take the surface of water as the reference, i set the Bernoulli's equation as:
[tex]P_o=P_o+ρgh+\frac{1}{2}ρv^2[/tex]
where v=flow velocity, ρ=density of fluid, h=3.6m and Po is the atmospheric pressure.
I don't think i will get an answer using the above equation. Please tell me where i am wrong.
 
  • #4
The height should be negative because it is below the reference level. What answer do you get then? I would like to also add that the flow takes into account the whole of the system - that is the flow at the top is the water from the whole of the surface of the container. The speed of the water molecules would then be very low due to the large surface area contributing to the flow - which we take to be zero.
 
Last edited:
  • #5
Basic_Physics said:
The height should be negative because it is below the reference level. What answer do you get then?
Oops, absolutely forgot that. I get my answer as 6√2 m/s as mentioned in the answer key.
I am stuck at b) part. I guess to find the discharge rate of flow, i need to use the equation Q=Av, where Q is rate of flow, A is cross-section area and v is the velocity of liquid. If i plug in the values A=64*10^(-3) m^2 and v=6√2 m/s, i don't get the answer mentioned in the answer key. Please tell me where i am wrong.

Thanks for the help.
 
  • #6
All error I can see is that 1 cm is 10-2 m so it so 10-4 m2 for A. Also it is r2 so it should be divided by 2 since it is the diameter.

To get the pressure at the crest you set BE up at the crest and at the surface of the water. The speed of the water at the crest will be the same as the exit speed calculated in (a) - the water flows with the same speed throughout the pipe. In this case the height is positive (above the zero level). I think the density of water is 103 kg/m3?
 
Last edited:
  • #7
Basic_Physics said:
All error I can see is that 1 cm is 10-2 m so it so 10-4 m2 for A.
I came to edit my post but you beat me. :tongue2:

To get the pressure at the crest you set BE up at the crest and at the surface of the water. The speed of the water at the crest will be the same as the exit speed calculated in (a) - the water flows with the same speed throughout the pipe. In this case the height is positive (above the zero level). I think the density of water is 103 kg/m3?
Using the BE, i get
[tex]P_o=P_A+ρgh+\frac{1}{2}ρv^2[/tex]
P_A is the pressure at A. Is this equation right?
 
  • #8
Yes, and it should be /4 not 2.
 
  • #9
Basic_Physics said:
Yes, and it should be /4 not 2.

If i plugin the values in my equation, i get the correct answer, thanks for the help Basic_Physics! :smile:
 

1. What is Bernoulli's equation and how does it relate to fluid mechanics?

Bernoulli's equation is a fundamental equation in fluid mechanics that relates the pressure, velocity, and height of a moving fluid. It states that at any point along a streamline, the sum of the pressure, kinetic energy, and potential energy per unit volume is constant. This equation is based on the principle of conservation of energy and is commonly used to analyze the behavior of fluids in motion.

2. How do I apply Bernoulli's equation to a fluid mechanics problem?

To apply Bernoulli's equation to a fluid mechanics problem, you first need to identify the points along the streamline where you want to calculate the pressure, velocity, and height. Then, you need to determine the values of each variable at those points. Finally, you can use the equation to solve for the unknown variables.

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

Bernoulli's equation is based on several assumptions, including that the fluid is incompressible, inviscid, and has a steady flow. It also assumes that the fluid is flowing along a streamline and that there is no energy loss due to friction or other external forces.

4. Can Bernoulli's equation be applied to all fluids?

Bernoulli's equation can be applied to most fluids, as long as the assumptions mentioned above hold true. However, it may not accurately predict the behavior of highly viscous or compressible fluids.

5. Are there any limitations to using Bernoulli's equation in fluid mechanics?

While Bernoulli's equation is a useful tool in fluid mechanics, it has some limitations. It can only be applied to ideal fluids, and it may not accurately predict the behavior of fluids in complex systems with turbulence or other external factors. Additionally, it is important to remember that Bernoulli's equation is just one part of the larger field of fluid mechanics and should be used in conjunction with other principles and equations.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Classical Physics
Replies
6
Views
960
Replies
204
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
18
Views
2K
Replies
8
Views
586
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Replies
1
Views
957
  • Introductory Physics Homework Help
Replies
16
Views
2K
Back
Top