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

[RGG]

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:

Thank you very very much once again !

 

[proton007007]

The (a) part can be solved by conserving volume of the liquid . (Think about rate of change of volume !)

 

[RGG]

heya, A was okay actually. The main problems I have are with B onwards !

Thank you for your viewership :)

 

[RGG]

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.A_b = U_b.A_f
Q = W.b = U_b.h

Therefore, U_b = 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: U_b/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 !