Fluid Dynamics Question(not too difficult)

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SUMMARY

The discussion focuses on calculating the range of water streams from spouts at heights of 10 cm, 20 cm, 30 cm, and 40 cm, with a maintained water level of 45 cm. The participant identifies that the spout at 20 cm provides the greatest range and calculates the velocity using the formula V = √(2gh), resulting in a velocity of 2.215 m/s. The participant seeks clarification on the appropriate formula to determine the range, considering options involving final and initial velocities and acceleration. The question is resolved with community assistance.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Familiarity with kinematic equations for projectile motion.
  • Basic knowledge of gravitational acceleration (g = 9.81 m/s²).
  • Ability to perform calculations involving square roots and algebraic manipulation.
NEXT STEPS
  • Study the derivation of the range formula for projectile motion.
  • Learn about the effects of varying spout heights on fluid dynamics.
  • Explore the application of Bernoulli's principle in real-world scenarios.
  • Investigate the impact of air resistance on projectile trajectories.
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Students studying fluid dynamics, physics enthusiasts, and educators looking to enhance their understanding of projectile motion and fluid behavior in containers.

bob24
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Homework Statement


The spout heights for a container are 10 cm, 20cm, 30cm, and 40cm. The water level is maintained at a 45 cm height by an outside supply. Which water steam has the greatest range relative to the base of the container.
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I know that the one at 20cm is the greatest range already. I want to find out the actual range though.


Homework Equations


V=radical(2gh)



The Attempt at a Solution



For 20 cm: V=radical(2gh)
V=radical(2*9.81*.25m)
V=2.215m/s
So I have the velocity but I am confused about how to find the range. Which formula do I use and what values go where?

Do I use: Vfinal^2 - Vinitial^2=2aS, with S being distance
OR
Sfinal=1/2aT^2+ViT+Si with T=time and S=distance
 
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UPDATE: Figured out the answer to my question, thanks :)
 

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