Cross section of a stream flowing from a hole

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SUMMARY

The discussion focuses on calculating the diameter of a water stream emerging from a cylindrical tank with a depth of 2.5 meters and a hole diameter of 1 mm. The continuity equation, expressed as v1a1 = v2a2, is essential for solving the problem. Participants emphasize that the velocity of the water stream changes as it falls, necessitating the application of fluid dynamics principles to determine the stream's diameter at a distance of 7.5 meters from the hole.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the continuity equation in fluid mechanics
  • Basic knowledge of kinematics and projectile motion
  • Ability to perform calculations involving area and velocity
NEXT STEPS
  • Study the application of the continuity equation in fluid flow scenarios
  • Learn about Bernoulli's principle and its implications for fluid velocity
  • Explore the concept of free fall and its effect on fluid streams
  • Investigate how to calculate the cross-sectional area of a stream at various distances
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Students studying fluid mechanics, engineers working with hydraulic systems, and anyone interested in the dynamics of fluid flow in practical applications.

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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 v_{1}a_2=v_2a_2, but I don't know how to start.

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

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