Which one of the following statement is correct regarding critica
| Which one of the following statement is correct regarding critical state of flow through a channel section?
A. Specific energy is a minimum for a given discharge
B. Specific energy is a maximum for a given discharge
C. The Froude number is greater than two
D. The discharge is a minimum for a given specific force
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
- In the following diagram, h1and h2 are the depths corresponding same specific energy. Hence are called alternate depths.
- Critical depth (hc) is defined as that depth of flow of water at which specific energy is minimum for given discharge.
We know, For rectangular channel
Specific energy, \({E_S} = h + \frac{{{q^2}}}{{2g{h^2}}}\)
Differentiating it with respect to depth of flow and equating to zero,
\(\frac{{dE}}{{dh}} = 0 \Rightarrow {h_c} = {\left( {\frac{{{q^2}}}{g}} \right)^{\frac{1}{3}}}\)
- Flow is said to be critical when Froude number is equal to 1.
\(\therefore {F_r} = \frac{{{Q^2}T}}{{g{A^3}}} = 1\)
Where, T-top width of the section of flow, A-area of c / s
- It should be noted that, at critical condition-
- Specific energy will be minimum for given discharge
- Maximum discharge for given specific energy
