Problem with rectangular and triangular weir

[Queren Suriano]

Homework Statement

A rectangular weir (Cd = 0.623) thin crest without lateral contraction of 1 meter in length and a triangular weir (theta = 90 °) are located on the same channel. If the apex of the triangular weir (Cd = 0.593) is 0.15 meters below the crest of the rectangular weir and neglecting the approach speed determine a) the load on landfills when landings are equal, b) If the discharge of the rectangular weir is greater, determine the load should be for differential flow is maximum

Homework Equations

Q( rectangular) =1.84 LH^(3/2) [/B]
Q(triangular)= 1.40H^(5/2)

The Attempt at a Solution

a)[/B]
Qrectangular = Q triangular
1.84 (1) H1^(3/2) =1.40H2^(5/2). H1: Load rectangular weir, H2: Load triangular weir
H1= H2 -0.15

1.2515(H2)^(5/3) -1.5(H2) =-0.2251
I have two answers:
H2=0.21, H2=1.04 m

Is it right??

b) I think I can derivate d(Qrec -Qtriangular) /dH =0
But I don't know if I derivate respect to H1 or H2

 

[KataKoniK]

I would like to offer some suggestions for solving this problem:

1. First, it would be helpful to clarify the problem statement. Is the question asking for the load on the landfills (i.e. the amount of water flowing over the weir) when the landings are equal, or is it asking for the height of the water (H1 and H2) when the landings are equal? This will affect your approach to solving the problem.

2. It would also be helpful to define the variables used in the equations. For example, what is L and what is theta? Clarifying this information will make it easier to follow your solution.

3. For part a), it seems like you are on the right track, but I am not sure where the value of 0.21 for H2 is coming from. Can you explain your reasoning for this value? It might also be helpful to check your units - are they consistent on both sides of the equation?

4. For part b), it would be helpful to define what differential flow means in this context. Does it refer to the difference in flow between the rectangular and triangular weirs, or does it refer to a specific flow rate? Once you have clarified this, you can then determine which variable (H1 or H2) should be used for the derivative.

Overall, my advice would be to double check your calculations and make sure your equations are properly defined and used. It might also be helpful to draw a diagram to visualize the problem and better understand the relationships between the variables. Good luck!