Bernoulli's law in a network of a tube and a reservoir

• Niles
In summary, the conversation discusses a system consisting of a reservoir and a long tube. The fluid in the reservoir has a non-zero velocity, but the velocity in the tube is assumed to be zero. There is a question about whether the pressure in the reservoir is lower than that in the tube due to the velocity difference, using Bernoulli's law. However, it is determined that Bernoulli's law only applies to fluid in the same streamline, and since the fluid in the reservoir and tube are in different streamlines, this cannot be concluded. The possibility of using the Venturi effect and the effect of gravity are also discussed, but ultimately disregarded due to the assumption of a flat system.
Niles

Homework Statement

I am looking at the following system:

It shows a pore/tube (B) which is attached to a reservoir A. The fluid in reservoir A has a non-zero velocity in the horizontal direction, but I assume that the tube B is so long that the velocity there is unaffected and still zero.

Based on Bernoulli's law, can I conclude that the pressure in reservoir A is lower than that in tube B due to the velocity difference?

Note that i neglect the effects of gravity etc., I assume the system is in a plane.

Niles said:
Based on Bernoulli's law, can I conclude that the pressure in reservoir A is lower than that in tube B due to the velocity difference?
I don't think so. Bernoulli's law is for a streamline. Fluid flowing in A and that residing in B are in different streamlines.
If the pipe A broadens further along and is then exposed to an ambient pressure also applying at the far end of B, you can invoke the Venturi effect.

If B is assumed to be long and therefore velocity 0, would there be a relative height in your Bernoulii equation that accounts for the weight of the fluid in B? Higher velocity in A would cause a the fluid in B to rise

EDIT: Nevermind I see you are neglecting gravity, did not read that part!

What is Bernoulli's law?

Bernoulli's law is a fundamental principle of fluid dynamics that states that in a steady flow of an ideal fluid, the total energy of the fluid remains constant. This means that as the fluid flows through a tube, the sum of its kinetic energy, potential energy, and internal energy remains the same.

How does Bernoulli's law apply to a network of a tube and a reservoir?

In a network of a tube and a reservoir, Bernoulli's law explains the relationship between the velocity and pressure of the fluid. As the fluid flows from the reservoir into the tube, its velocity increases and its pressure decreases due to the conservation of energy. When the fluid reaches the end of the tube and enters the reservoir again, its velocity decreases and its pressure increases, returning to its initial values.

What is the significance of Bernoulli's law in a network of a tube and a reservoir?

Bernoulli's law is significant in understanding fluid flow in various systems, including the network of a tube and a reservoir. It allows us to predict the behavior of fluids in these systems and make calculations related to pressure, velocity, and flow rate. This law is widely used in engineering and plays a crucial role in the design and operation of many devices and systems.

What are the assumptions of Bernoulli's law?

Bernoulli's law is based on several assumptions, including that the fluid is incompressible, inviscid, and irrotational. It also assumes that there is no energy loss due to friction, the flow is steady, and the fluid's density is constant. These assumptions allow for simplified calculations and predictions of fluid behavior, although in real-world scenarios, they may not always hold true.

How is Bernoulli's law related to the Venturi effect?

The Venturi effect is a phenomenon that occurs when a fluid flows through a narrow section of a tube, causing its velocity to increase and its pressure to decrease. This effect is based on Bernoulli's law, as the conservation of energy results in a decrease in pressure as the fluid's velocity increases. The Venturi effect is used in various applications, such as carburetors in engines and air flow meters in heating and cooling systems.

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