Where Am I Going Wrong in My Fluid Mechanics Faucet Problem?

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SUMMARY

The discussion centers on calculating the diameter of a water stream from a kitchen faucet using fluid mechanics principles. The user applies the continuity equation, A1V1 = A2V2, and attempts to derive velocities from the given volume of 125 cm³ filled in 16.3 seconds. The user correctly identifies the need to calculate average velocity but struggles with the application of the equations of motion and the correct conversion of units. The solution requires precise calculations of velocities and areas to find the diameter at a specific height below the faucet.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically the continuity equation.
  • Knowledge of kinematic equations for motion under gravity.
  • Ability to perform unit conversions, particularly between centimeters and meters.
  • Familiarity with basic calculus concepts related to area and volume calculations.
NEXT STEPS
  • Calculate average velocity using the formula V = Volume / Time for the given volume of 125 cm³ over 16.3 seconds.
  • Learn about the application of Bernoulli's equation in fluid flow problems.
  • Explore the relationship between pressure, velocity, and area in fluid dynamics.
  • Study the effects of gravitational acceleration on fluid flow and its impact on velocity calculations.
USEFUL FOR

Students and professionals in engineering, particularly those studying fluid mechanics, as well as anyone involved in practical applications of fluid flow calculations, such as plumbing engineers and hydraulic designers.

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a stream of water in steady flow from a kitchen faucet. at the faucet the diameter of the stream is .96cm the stream fill a 125cm^3 conaienr in 16.3s find the diamiter if the stream 13cm below he opening if the faucet
i know that A1V1 = A2V2 = constant so pi *.49^2 *V1= pi r^2 *V2
how do i get the velocitys from (125cm^3 in 16.3s) to me that is the average v??
 
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HINT:

\rho A v

is the volume of liquid that passes through a given area per unit time.
 
this is what i do and still don't get the right answer
solve for v with pAv =125cm^3/16.3s with p= density of water A= area of stream at the faucet so v = v1
with v1 i solve for v2 with v2^2 = v1+ 2 a (xf- xi)
having both velocitys i use A1v1=A2v2 and A2=pi * r^2 i to solve for r
i also change r1 to .0048m delta x to -.13m a=-9.8 when solving for v and vf where am i going wrong??
 

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