Fluid Mechanics: Bernoulli & Energy Equations Problem- Help?

In summary: Please start a new thread for this. Also, please put it into Engineering and Computer Science homework forum, and use the homework template. Thanks.
  • #1
hdp12
68
2
Hello there. I took a test yesterday in my thermal fluids 1 class and I was hoping somebody could confirm or critique my answer. (Don't worry, I asked the professor first if I could take the picture)

The problem is:
Water is pumped from a lake to a pool through a 0.05 m diameter pipe. System friction losses are hf = 50V2/(2g), where V is the average velocity in the pipe. If the power of the pump is 10 kW, what is the mass flow rate pumped?
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The diagram given with the problem is attached as well as the two pages of my work. I was fairly certain that I messed up on the first page so I redid it on the second page and hope that it was the correct approach. Thermodynamics & Fluid Mechanics are tough for me because you really have to know exactly how, when, why, and which formulas to use at precisely the correct time. If somebody could just look over my work and let me know if I was on the right track, what my errors were, and/or the correct approach, I'd really appreciate it!

Thanks,
H.
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  • #2
It looks like you have been trying to use two versions of an equivalent equation:

1. The open system (control volume) version of the first law of thermodynamics (page 1)
2. The Bernoulli equation, modified to include pump work and friction energy losses (page 2)

Given that the friction loss is given with a g in the denominator, my inclination is that they meant for you to use method 2. For the Bernoulli version, I recommend using point 1 before the inlet of the pump (so p1=0 and v1 = 0) and point 2 (after the outlet in the pool (so p2=0 and v2 = 0); so,
$$h_{pump}=(z_2-z_1)+h_L$$
This is what you ended up with, and, given the rest is straightforward, it looks like you did it right.
 
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  • #3
Chestermiller said:
This is what you ended up with, and, given the rest is straightforward, it looks like you did it right.

That is very good news! They take forever grading the tests and I just really wanted some positive feedback. If it's not too much to ask, would you tell me if I did the second question correctly too? There are only 2 questions so I promise this is the last one!

2hxmuiv.jpg

2djoqb5.jpg

333cy0j.jpg
 
  • #4
hdp12 said:
That is very good news! They take forever grading the tests and I just really wanted some positive feedback. If it's not too much to ask, would you tell me if I did the second question correctly too? There are only 2 questions so I promise this is the last one!

2hxmuiv.jpg

2djoqb5.jpg

333cy0j.jpg
Please start a new thread for this. Also, please put it into Engineering and Computer Science homework forum, and use the homework template. Thanks.
 

1. What is Bernoulli's equation and how is it used in fluid mechanics?

Bernoulli's equation is a fundamental equation in fluid mechanics that describes the relationship between fluid pressure, velocity, and elevation in a flowing fluid. It states that in an ideal fluid, the sum of the fluid's kinetic energy, potential energy, and pressure energy remains constant at any point along a streamline. This equation is commonly used to solve problems involving fluid flow, such as calculating the velocity of a fluid at a specific point or determining the pressure difference between two points in a pipe or channel.

2. How is the Bernoulli equation derived?

The Bernoulli equation is derived from the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed. In fluid mechanics, this means that the total energy of a fluid remains constant as it flows. The Bernoulli equation is a simplified version of this principle that takes into account the specific energies of a fluid, including its kinetic, potential, and pressure energies.

3. What is the difference between steady and unsteady flow in fluid mechanics?

Steady flow refers to a fluid in which the velocity, pressure, and other properties do not change with time at any point in the flow. This type of flow is often encountered in water or air flowing through pipes or channels. Unsteady flow, on the other hand, is a type of flow in which the fluid properties vary with time at a certain point or throughout the flow. This can occur in situations like a sudden change in flow rate or the presence of turbulence in the fluid.

4. Can the Bernoulli equation be applied to real-world fluid systems?

While the Bernoulli equation is a useful tool for solving fluid mechanics problems, it is important to note that it is based on several assumptions, such as the fluid being ideal and incompressible, and the flow being steady and laminar. In real-world fluid systems, these assumptions may not hold, and the equation may need to be modified or used in conjunction with other equations. However, the Bernoulli equation can still provide valuable insights and approximations for real-world situations.

5. How does the energy equation relate to the Bernoulli equation?

The energy equation is a more general form of the Bernoulli equation that takes into account all forms of energy in a fluid system, including heat, work, and mechanical energy. It is used to analyze the total energy balance in a fluid system, whereas the Bernoulli equation only considers specific forms of energy. The Bernoulli equation is a simplified version of the energy equation that is often used in specific scenarios, such as when the fluid is incompressible and the flow is steady and inviscid.

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