The critical depth (hc) is given by, where q = Rate of flow per unit width of channel
- A(q²/g)1/2
- B(q/g)1/3
- C(q²/g)1/3Correct
- D(q²/g)2/3
Solution
Concept
Critical depth formula in open channel flow
Formula
hc = (q2/g)1/3
Step-by-step solution
1. Critical flow condition in open channel flow occurs when specific energy is minimum for a given discharge. 2. For a rectangular channel, critical depth hc is related to unit discharge q by the formula q2 / g = hc3. 3. Solving for critical depth gives hc = (q2 / g)1/3. Answer: C
Explanation
In open channel hydraulics, critical depth occurs when the specific energy of the flow is minimized for a given discharge rate. Mathematically, setting the derivative of specific energy with respect to depth equal to zero yields the equation hc = (q²/g)1/3. This makes option C the correct expression for critical depth in a rectangular channel.
Why the other options are wrong
A) The flow rate per unit width must be raised to the power of 2 and overall bracket to 1/3. B) The flow rate per unit width q must be squared in the critical depth equation. D) The exponent 2/3 is incorrect as critical depth depends on the cube root of q²/g.
Shortcut
Critical depth hc = (q²/g)1/3: remember power 2 on q inside a cube root (1/3).
Common mistake
Confusing the exponent of the critical depth formula (1/3) with (1/2) or (2/3).
Correct answer: C) (q²/g)^(1/3)
