How to estimate the performance of a pump using Navier Stokes?

In summary, the conversation involves someone asking for feedback on their attempt at a homework problem and another person confirming that the approach looks reasonable and correct. They also mention that they will check back later for a more thorough review and suggest involving someone else with a background in fluids. Upon a detailed review, the approach is deemed correct, though there is a minor suggestion to keep a factor in the equation.
  • #1
owlwise2010
2
0
Homework Statement
Fluid Mechanics Homework:
Flows between two horizontal parallel plates
apart. The upper plate is moving with a uniform speed U, while the lower one is kept stationary. A constant pressure gradient of dp/dx is applied
Relevant Equations
Navier Stokes and Volumetric flow
Hello everyone,
Attached is the homework problem (FluidHmk.PNG) as well as the attempt (Attempted 1 and 2).

Just wanted to know if this is method to approach the problem

Thanks in advance.
 

Attachments

  • FluidHmk.PNG
    FluidHmk.PNG
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  • Attempted.PNG
    Attempted.PNG
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  • Attempted2.PNG
    Attempted2.PNG
    51.9 KB · Views: 338
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  • #2
Your approach looks very reasonable to me based on a quick glance over everything. I don't have time right now to actually go through and check the numbers, but it seems that you've taken the correct view of the problem, and nothing jumps out at me as being obviously incorrect.

I'll try to check back later this evening when I have more time to actually look over it in more depth if nobody else has a chance. In the meantime, maybe @boneh3ad has time to take a look (he's one of the only other people I'm aware of on the forum with a fluids background)?
 
  • #3
I finally got a chance to go through in more detail, and it all looks correct to me. I might have left the factor of l in a while longer rather than just calling it 1, but the problem statement didn't actually specify that it needed to be in terms of l (and it fundamentally doesn't change anything about the problem), so this seems fine to me.
 

1. How does Navier Stokes equation help in estimating pump performance?

The Navier Stokes equation is a fundamental equation in fluid mechanics that describes the motion of a fluid. By applying this equation to the design of a pump, we can estimate its performance by calculating the flow rate, pressure, and efficiency of the pump.

2. What parameters are needed to estimate the performance of a pump using Navier Stokes?

To estimate the performance of a pump using Navier Stokes, we need to know the properties of the fluid being pumped, such as density and viscosity, as well as the geometry of the pump, including the inlet and outlet sizes, impeller diameter, and blade angles.

3. Can Navier Stokes accurately predict pump performance?

Navier Stokes equation is a highly accurate mathematical model that can accurately predict the performance of a pump. However, it is important to note that there may be some discrepancies between the theoretical calculations and the actual performance of the pump due to factors such as friction and turbulence in the real world.

4. How can we validate the estimated performance of a pump using Navier Stokes?

The estimated performance of a pump using Navier Stokes can be validated through experimental testing. By comparing the calculated values with the actual performance of the pump in a controlled environment, we can determine the accuracy of the estimated performance.

5. Are there any limitations to using Navier Stokes for pump performance estimation?

While Navier Stokes equation is a powerful tool for estimating pump performance, it does have some limitations. It assumes that the flow is steady, incompressible, and inviscid, which may not always be the case in real-world scenarios. Additionally, it may not account for all the complexities of pump design, such as cavitation and wear.

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