Question

What are the steps to compute critical depth for a non-rectangular channel?

Answer 1

Consider any non rectangular channel for example triangular channel

Following are the steps to calculate critical depth in non rectangular channel.

1. Specific energy is defined as:

• E=d+u2/2g, where = cross-sectionally averaged velocity,

2. Noting that, u = Q/A

3. Substituting in energy equation

• E= d + Q2/2gA2

4. Find the minimum energy for a given Q; note that A=A(d)

• dE/dD = (1-Q2)/2g(2 dA/A3 dd) = 0

Set equal to zero and solve for the critical value of d(dc)

We note that dA = wdd = dA/dd =w, where w = width of the water surface.

5. Thus,

1-(Q2/2g) (2/A3) x w|d-dc = 0

6. Finally, we establish the relationship between Q, g, A and w at critical flow:

Q2/g = (A3/w)d = dc

For a given cross section, the right hand side is a function of d only. Noting that

Q = Ac x uc

Substituting

(Ac2 uc2)/g = A3/Wc

uc2 = gAc/wc

uc = (gAc/wc)

corresponding to uc, dc then can be calculated.

Thanks