How can the Bernoulli Equation be applied to solve a challenging problem?

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SUMMARY

The discussion focuses on applying the Bernoulli Equation to solve a fluid dynamics problem involving the conservation of volume and flow rates. The equation presented is V²/2g + p/dg + z = constant, where V represents velocity, g is the acceleration due to gravity, p is pressure, d is density, and z is elevation. The user successfully derived expressions for discharge and velocity but struggles with further application of the equation in specific scenarios. The conversation emphasizes the importance of understanding fluid flow principles and the implications of the Bernoulli Equation in practical problems.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the Bernoulli Equation
  • Knowledge of conservation of mass and volume in fluid systems
  • Basic calculus for analyzing flow rates and changes
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  • Study the derivation and applications of the Bernoulli Equation in various fluid flow scenarios
  • Explore the concept of discharge and its calculation in fluid systems
  • Learn about the implications of pressure and elevation changes in fluid dynamics
  • Investigate real-world applications of the Bernoulli Equation in engineering and environmental contexts
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Students in engineering or physics, fluid dynamics enthusiasts, and professionals working in hydraulics or related fields will benefit from this discussion.

RGG
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Hey everyone ! I'm new here and found that this forum was very useful. Would really appreciate it if you could help me out with this problem ! Have been scratching my head for hours now :(

Question:
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Thank you very very much once again !
 

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The (a) part can be solved by conserving volume of the liquid . (Think about rate of change of volume !)
 
heya, A was okay actually. The main problems I have are with B onwards !

Thank you for your viewership :)
 
Okay, so I was told that my homework request was an unreasonable one and hence, I have looked through the forum rules. I shall abide by them ! So sorry for being ignorant.

Homework Statement


See Above

Homework Equations


Bernoulli Equation: V2/2g + p/dg + z = constant
V = velocity of particles flowing through that point of the streamline
g = acceleration due to gravity
p = pressure at that point of the streamline
d = density
z = elevation at that point of the streamline

The Attempt at a Solution



(a) V = H0B = bh + (B-b)H
H=(BH0-bh)/(B-b)

(b) By conservation of volume,
Discharge, Q = W.Ab = Ub.Af
Q = W.b = Ub.h

Therefore, Ub = bW/h

(c) Since gap-averaged flow from x=0 to x=b is a well-behaved flow, dU(x)/dx = 0

(d)
At point x=b: Ub/2g + dg(H-h)/dg + h = constant

From here, I'm really not too sure how to proceed.

Any help would be greatly appreciated ! Thank you !
 

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