Navier Stokes Thm Homework: Equations & Solutions

In summary, the conversation discusses an oversight in a mathematical equation involving the constant ##C_1## and the height of liquid, which was mistakenly omitted earlier in the equation. The mistake was pointed out and clarified, and further clarification was given regarding the potential energy and the inclusion of the ##sin (\alpha)## factor.
  • #1
yecko
Gold Member
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Homework Statement


螢幕快照 2018-04-25 下午8.44.18.png
[/B]
螢幕快照 2018-04-25 下午8.44.41.png


Homework Equations


Navier strokes theorem

The Attempt at a Solution


May I ask why would there suddenly a "h" in the highlighted part?
"h" wasnt existed in the previous steps, which C2=0 shouldn't add height of the liquid as a constant in the formula...
thanks
 

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  • #2
The oversight occurs earlier, where it should say:

So that the constant in Eqn (2) is
##C_1\ =\ \dfrac{\rho g}\mu h\sin α##
 
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Likes yecko and jedishrfu
  • #3
That's following the ##U## being potential energy and so extending the ##U = mgh## to factor in the ##sin (\alpha)## right?
 
  • #4
I followed the maths until I saw where the author had forgotten to transcribe an h.
 

FAQ: Navier Stokes Thm Homework: Equations & Solutions

What is the Navier-Stokes theorem?

The Navier-Stokes theorem is a fundamental equation in fluid mechanics that describes the motion of a fluid. It is named after Claude-Louis Navier and George Gabriel Stokes, who independently derived the equation in the 19th century.

What are the equations involved in the Navier-Stokes theorem?

The Navier-Stokes theorem consists of two equations: the continuity equation and the Navier-Stokes equation. The continuity equation describes the conservation of mass in a fluid, while the Navier-Stokes equation describes the conservation of momentum.

What are some real-world applications of the Navier-Stokes theorem?

The Navier-Stokes theorem has numerous applications in various fields such as aerodynamics, weather forecasting, oceanography, and even in the design of everyday objects like pipes, pumps, and turbines. It is also used in the simulation of fluid flow in computer graphics and video games.

What are the main challenges in solving Navier-Stokes equations?

The Navier-Stokes equations are highly complex and nonlinear, making them difficult to solve analytically. Even with the use of numerical methods, solving these equations accurately can be computationally intensive and time-consuming. Additionally, the equations are sensitive to initial and boundary conditions, making it challenging to model real-world scenarios accurately.

Are there any known solutions to the Navier-Stokes equations?

There are a few known exact solutions to the Navier-Stokes equations, but they are limited to simplified scenarios. In most cases, numerical methods are used to approximate solutions to these equations. These methods involve dividing the fluid into small cells and solving the equations at each of these cells, using mathematical techniques such as finite difference or finite element methods.

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