Cross section of a stream flowing from a hole

In summary, the problem involves a cylindrical tank filled with water and a small hole at the bottom where the water emerges. The diameter of the hole is 1 mm and the water stream decreases in diameter as it falls. The task is to find the diameter of the water stream at a distance of 7.5 m from the hole. The continuity equation, v1a2=v2a2, may be used to solve the problem, but the velocity of the water stream may not remain constant after leaving the tank.
  • #1
rbwang1225
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Homework Statement



Consider a cylindrical tank filled with water with 2.5-m depth. The water emerges from a small hole at the center of the bottom, as shown in the figure. The diameter of the hole is 1 mm. The cross-section area of the vertical water stream decreases as it falls. Find the diameter of the water stream at the position 7.5 m from the hole.
cylinder.jpg


Homework Equations



I think I have to address the continuity equation [itex]v_{1}a_2=v_2a_2[/itex], but I don't know how to start.

Any help would be appreciated.
 
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  • #2
Hint: After the stream leaves the tank, does its velocity remain constant?
 

Related to Cross section of a stream flowing from a hole

What is a cross section of a stream?

A cross section of a stream is a representation of the stream's profile or shape at a particular location or point. It shows the stream's width, depth, and bottom characteristics.

What causes a stream to flow from a hole?

A stream flowing from a hole is usually the result of groundwater discharging from an underground aquifer through an opening or crack in the surface. This can also occur when a stream or river flows underground and resurfaces through a hole.

How does the cross section of a stream affect its flow?

The cross section of a stream plays a crucial role in determining the flow of the stream. A wider and deeper cross section allows for a larger volume of water to flow through, while a narrower and shallower cross section restricts the flow. The bottom characteristics also affect the flow by creating turbulence or obstacles.

What can we learn from studying the cross section of a stream?

Studying the cross section of a stream can provide important information about the stream's discharge rate, velocity, and potential for flooding. It can also give insights into the geological and hydrological processes that have shaped the stream's profile.

How is the cross section of a stream measured?

The cross section of a stream can be measured through various methods, including using a surveying instrument such as a total station or measuring the water's depth and width at several points along the stream. Remote sensing techniques, such as LiDAR, can also be used to create a detailed cross section of a stream.

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