# How do I incorporate theta into the momentum equation for Fluids homework?

In summary, the conversation discusses the application of the conservation of momentum equation in a fluid mechanics problem involving a wedge. The equation is modified to incorporate the angle theta and the problem is divided into upper and lower right triangles to simplify calculations. The concept of momentum per unit length is also introduced and discussed. There is a discussion about a mistake in the calculation due to not paying attention.

## Homework Equations

$$\sum(\dot{m}\vec{v})_{exit}-\sum(\dot{m}\vec{v})_{inlet}=\sum F_{ext}$$

I only know that this is cons of momentum because my prof told us. I am having a hard time visualizing how to incorporate THETA into the above equation since it is not a nice right triangle.

I am thinking that since the exit velocities are equal, than the inlet flow must be being split about the wedges horizontal axis of symmetry.

Thus, I think I can divide the wedge into an "upper" and "lower" right triangle whose angle wrt to the horizontal is $\frac{\theta}{2}$.

Then I can resolve the momentum eq into Cartesian coordinates.

Sound good?

Sounds lovely!

Nice! I guess that what is confusing me now, is why they gave me
force/unit length into page

But I am just going to start plugging in and see what happens.

I guess that what is confusing me now, is why they gave me
force/unit length into page
Consider it to be an arbitrarily wide sheet of water. Use momentum per unit length as well.

Doc Al said:
Consider it to be an arbitrarily wide sheet of water. Use momentum per unit length as well.

Okay, so the m-1 just drops out anyway, and this problem reduces to regular cons of mom

Yep.

Thanks! 83.4 degrees sounds reasonable I think

83.4 degrees sounds reasonable I think
Show how you got that answer.

Rethink your result for m, the mass flow rate. You want it to be mass flow per unit width (or depth).

I am not sure that I follow. Errr... Okay. So that inlet with the 4 cm dimension is NOT a PIPE...right?

It is a "sheet" with area 4cm*WIDTH. Thus my, mass flow rate should be, with h=4cm:

$$\dot{m}=\rho V (h*W)\Rightarrow \frac{\dot{m}}{W}=\rho Vh$$

Am I with you now?

Now you're cooking.

Typical 'not-paying-attention' mistake. Perhaps I should turn off Band of Brothers while I do my studies?

Thanks Doc!

## 1. What is the conservation of momentum?

The conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant. This means that in any interaction between two or more objects, the total momentum before and after the interaction is the same.

## 2. How does the conservation of momentum apply to fluids?

In fluids, the conservation of momentum is used to describe the motion of fluids and the forces acting on them. When a fluid is in motion, its particles have momentum, and this momentum is conserved as the fluid moves. This principle can be applied to explain fluid flow and pressure in various systems, such as pipes and pumps.

## 3. What are some practical applications of the conservation of momentum in fluids?

The conservation of momentum in fluids is used in many real-world applications, such as in the design of airplane wings and the flow of air around them, the workings of hydraulic systems, and the motion of fluids in the human body, such as blood flow and breathing.

## 4. What are the limitations of the conservation of momentum in fluids?

While the conservation of momentum is a powerful principle, it does have some limitations. It assumes that the fluid is incompressible and has a constant density, which is not always the case in real-world situations. Additionally, it does not take into account external forces such as friction, which can affect the motion of fluids.

## 5. How does the conservation of momentum relate to other principles, such as the conservation of energy?

The conservation of momentum is closely related to the conservation of energy, as both principles deal with the preservation of physical quantities. In fact, the conservation of momentum can be derived from the conservation of energy in certain situations, such as in elastic collisions. However, the two principles are not interchangeable, and they each have their own unique applications and limitations.

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