Simple Fluid mechanics (bernoulli's?)

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Discussion Overview

The discussion revolves around a fluid mechanics problem involving Bernoulli's principle, specifically analyzing the pressure inside a can of Coca-Cola with a pinhole leak that causes the liquid to spray vertically to a height of 0.5 m. Participants explore the application of Bernoulli's equation and the assumptions necessary to solve for the pressure.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the problem and applies Bernoulli's equation, making assumptions about the heights and pressures involved.
  • Another participant suggests considering the speed of the liquid at different points, prompting a discussion about the velocity at the hole and inside the can.
  • A later reply clarifies that the velocity at point 1 (inside the can) is assumed to be zero, correcting an earlier misunderstanding about the exit velocity.
  • There is a reiteration that the pressure term in Bernoulli's equation is exchanged for potential energy as one moves from the bottom to the top of the can.

Areas of Agreement / Disagreement

Participants generally agree on the assumption that the velocity inside the can is zero, but there is no consensus on how to fully resolve the problem or the implications of this assumption on the overall analysis.

Contextual Notes

The discussion does not resolve the overall pressure calculation, and assumptions about the velocities and pressures are based on the specific conditions of the problem. The dependence on the definition of the reference points in Bernoulli's equation is also noted.

mechEstudent
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Homework Statement



A can of Coca‐Cola has a small pinhole leak in it. The Coke sprays vertically
into the air at a height of 0.5 m. What is the pressure inside the can?
ρ = 1.11 g/mL

Homework Equations



Bernoulli: p1/ρ + (v1^2)/2 +g*z1 = p2/ρ + (v2^2)/2 +g*z2

The Attempt at a Solution



I've assumed:
z1=0, z2= 0.5
p2= atmospheric = 0 (gage)
v2=0

This simplifies bernoulli's to p1 = (g*z2-(v1^2)/2)/ρ
However v1 is still unknown and i have no way to solve for it
 
Last edited:
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mechEstudent said:

Homework Statement



A can of Coca‐Cola has a small pinhole leak in it. The Coke sprays vertically
into the air at a height of 0.5 m. What is the pressure inside the can?
ρ = 1.11 g/mL

Homework Equations



Bernoulli: p1/ρ + (v1^2)/2 +g*z1 = p2/ρ + (v2^2)/2 +g*z2


The Attempt at a Solution



I've assumed:
z1=0, z2= 0.5
p2= atmospheric = 0 (gage)
v2=0

This simplifies bernoulli's to p1 = (g*z2-(v1^2)/2)/ρ
However v1 is still unknown and i have no way to solve for it

Pretend you're a tiny bug just under the top surface of the can (where the hole is). How fast would you be moving? Or if you were at the bottom of the can?
 
Try to find v_1 from the simple equations of motion, in fact we have here the case of a vertical throw upwards.
 
ah, i see now that v1=0 as well, since point 1 is to be taken inside the can. I was mistakenly assuming v1 to be an exit velocity. i knew it was something simple. Thank you
 
mechEstudent said:
ah, i see now that v1=0 as well, since point 1 is to be taken inside the can. I was mistakenly assuming v1 to be an exit velocity. i knew it was something simple. Thank you

Correct! v1 = 0 everywhere inside the can. Inside the can, the pressure term in Bernoulli is exchanged for potential energy as we go from the bottom of the can to the top. But v1 = 0 everywhere inside.
 

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