Formula of energy per unit weight

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SUMMARY

The discussion centers on the application of Bernoulli's equation in fluid dynamics, specifically regarding a scenario with two exits from a streamline. Participants clarify that Bernoulli's equation applies to a single streamline, which can only have one entry and one exit, thus necessitating the consideration of only one exit at a time. The pressure difference and height difference are consistent across both exits, leading to the conclusion that the velocities at both exits will be the same, assuming atmospheric pressure at both points.

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  • Understanding of Bernoulli's equation in fluid dynamics
  • Knowledge of streamline flow concepts
  • Familiarity with pressure and velocity relationships in fluids
  • Basic principles of atmospheric pressure
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  • Study the derivation and applications of Bernoulli's equation in various fluid flow scenarios
  • Explore the concept of streamline analysis in fluid mechanics
  • Investigate the effects of varying velocities at multiple exits in fluid systems
  • Learn about pressure measurement techniques in fluid dynamics
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Students and professionals in engineering, particularly those specializing in fluid dynamics, as well as anyone involved in analyzing fluid flow systems with multiple exits.

foo9008
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Homework Statement


is the equation in the 3rd photo wrong ? since there are 2 exits , why shouldn't the eqaution become (P1 / y) + z + (8.33^2) / (2x9.81) = 0 + z +[ 2 (12^2) / (2x9.81) ] ?

Homework Equations

The Attempt at a Solution

 

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Bernoulli's equation is in respect of one streamline. A given streamline can only have one entry and one exit.
 
haruspex said:
Bernoulli's equation is in respect of one streamline. A given streamline can only have one entry and one exit.
but there are 2 exit, just consider 1 exit and ignore the another 1 ? how if the velocity at the 2 exit are different ?
 
foo9008 said:
but there are 2 exit, just consider 1 exit and ignore the another 1 ? how if the velocity at the 2 exit are different ?
Bernoulli's equation is telling you they would be the same velocity. Consider two streamlines, one from the inlet to one outlet, and one to the other outlet. Same pressure difference, same height difference.
 
haruspex said:
Bernoulli's equation is telling you they would be the same velocity. Consider two streamlines, one from the inlet to one outlet, and one to the other outlet. Same pressure difference, same height difference.
how do you know that the difference in pressure are the same?
 
foo9008 said:
how do you know that the difference in pressure are the same?
The third attachment says the pressure is atmospheric at both exits.
 
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