Law of continuity problem in fluids

In summary, when a hose with running water is partially blocked, the water velocity increases due to the law of continuity in incompressible fluids. However, when a tap is partially closed, the water velocity decreases due to the compressible nature of the valve design. This phenomenon cannot be explained by the law of continuity for incompressible fluids.
  • #1
Dingu Sagar
2
0
When a hose with running water is partially blocked with our finger ,the water comes out with a greater velocity. This is in agreement with the law of continuity in fluids which states that velocity of fluid is inversely proportional to the area of cross section.

But when a running tap is closed partially , the water velocity decreases even though the area has been reduced by the tap. Why is the phenomenon not explainable by the above law ?
 
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  • #2
Dingu Sagar said:
When a hose with running water is partially blocked with our finger ,the water comes out with a greater velocity. This is in agreement with the law of continuity in fluids which states that velocity of fluid is inversely proportional to the area of cross section.
The law of continuity doesn't state that exactly. What is marked in bold is true only if the flow of fluid is incompressible i.e the fluid density remains constant with respect to time.

But when a running tap is closed partially , the water velocity decreases even though the area has been reduced by the tap. Why is the phenomenon not explainable by the above law ?
That happens because the valve in the tap is designed in such a way as to make the flow compressible .
 

Related to Law of continuity problem in fluids

What is the law of continuity problem in fluids?

The law of continuity in fluids is a fundamental principle in fluid mechanics that states that the mass flow rate of a fluid remains constant throughout a pipe or channel, even if the cross-sectional area changes. This means that the product of the fluid velocity and cross-sectional area remains constant.

Why is the law of continuity important?

The law of continuity is important because it helps us understand how fluids behave in different situations. It allows us to predict the behavior of fluids in pipes, channels, and other systems, and is essential in the design and operation of many engineering systems, such as pumps, turbines, and pipes.

What is the equation for the law of continuity?

The equation for the law of continuity is A1v1=A2v2, where A represents cross-sectional area and v represents fluid velocity. This equation shows that as the cross-sectional area decreases, the fluid velocity must increase to maintain a constant mass flow rate.

What is an example of the law of continuity in action?

An example of the law of continuity is the flow of water through a pipe with a varying diameter. As the diameter of the pipe decreases, the water velocity must increase to maintain a constant flow rate. This is why water can shoot out of a garden hose with greater force when you partially cover the opening with your thumb.

Are there any exceptions to the law of continuity?

The law of continuity holds true for incompressible fluids, but it does not apply to compressible fluids (such as gases) where density can change. Additionally, the law of continuity assumes that the fluid is flowing without any external forces acting on it, such as gravity or wind. These factors can affect the behavior of fluids and may result in deviations from the law of continuity.

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