Fluid mechanics problem involving a hose and water coming out.

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Discussion Overview

The discussion revolves around a fluid mechanics problem involving a hose and the flow of water through it. Participants explore concepts related to conservation of mass and volumetric flow rates, as well as the implications of velocity distribution in the water stream. The scope includes theoretical reasoning and mathematical modeling related to fluid dynamics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant suggests using conservation of mass, proposing the equation V1*A1=V2*A2 for steady state incompressible fluid flow, but expresses uncertainty about the velocity distribution of the water stream.
  • Another participant agrees with the inclusion of conservation of volume but challenges the initial equation, stating that the flow through A1 varies with radius and suggesting a focus on total volumetric flow rates.
  • A participant seeks clarification on calculating volumetric flow rates, proposing to use the average velocity multiplied by the area of the tube and then relating it to the area of the water stream.
  • One participant computes an average flow per unit time and finds it to be (4/3)Vavg, indicating a discrepancy and suggesting the use of Bernoulli's principle to find the uniform velocity of the stream exiting at Dout.
  • Another participant introduces the idea of momentum conservation, suggesting to write integrals for momentum at the nozzle and downstream, equating them to solve for diameter ratios.

Areas of Agreement / Disagreement

Participants generally agree on the importance of conservation principles in fluid mechanics, but there are differing views on the correct application of these principles, particularly regarding the velocity distribution and the equations to use. The discussion remains unresolved with multiple competing approaches presented.

Contextual Notes

Participants express uncertainty regarding the velocity distribution and the implications of their calculations, particularly in relation to the average flow and the assumptions made about the flow conditions.

guitar24
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Homework Statement



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Homework Equations



I am having some trouble starting this problem. At first look I would say that a conservation of mass will give V1*A1=V2*A2 for steady state incompressible fluid. Then I would solve for A2 and relate the two diameters but I don't have the velocity distribution of the water stream. Any hints??
 
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You're spot on to include conservation of volume, but V1*A1 = V2*A2 can't be right since the flow of water thru A1 varies with r. So think of the total volume of water flowing in 1 sec. thru A1 and equate that to the total volume of water flowing in 1 sec. thru A2.
 
Thank you for your reply! could you elaborate a bit more on how I would do that?
The total volumetric flow rate in the tube is Vavg*Area of the tube. Multiply by one and you get the volume of water entering the cross section in one second. Then i would just divide that by the area of the water stream to get the volume of water flowing in one sec through the area of the water stream. Then just rearrange the equation to get Dout/Dhose. Is that correct?

Thank you!
 
guitar24 said:
Thank you for your reply! could you elaborate a bit more on how I would do that?
The total volumetric flow rate in the tube is Vavg*Area of the tube. Multiply by one and you get the volume of water entering the cross section in one second. Then i would just divide that by the area of the water stream to get the volume of water flowing in one sec through the area of the water stream. Then just rearrange the equation to get Dout/Dhose. Is that correct?

Thank you!

I computed the average flow per unit time and found it to be not Vavg but (1/R)∫v(r)dr with limits 0 and R, = (4/3)Vavg which is somewhat weird.

Anyway, whatever average V is, you are right in using mass conservation flow to get the answer. But you still need to get v, the (uniform) velocity of the stream exiting at Dout. For that, go to Bernoulli.
 
Given the assumption that there is no interaction with the surrounding air and thus no momentum loss, that suggests momentum is constant. Write integrals representing the momentum at the nozzle using the given velocity profile and one for the region downstream (utilizing conservation of mass flow) where the velocity is uniform. Equate them and solve for diameter ratios.
 

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