Question

When a supercritical stream enters a mild-sloped (M) channel section, the type of flow profile would become 

• A. M$_1$
• B. M$_2$
• C. M$_3$
• D. M$_1$ and M$_2$

Hint:

For mild slopes: - $y > y_n \Rightarrow$ M$_1$, - $y_c < y < y_n \Rightarrow$ M$_2$, - $y < y_c \Rightarrow$ M$_3$. Supercritical flow always corresponds to M$_3$ on mild slopes.

Answer 1

The Correct Option is C

Step 1: Recall the classification of flow profiles in gradually varied flow (GVF).
- Flow profiles depend on: (i) The slope of the channel (mild, steep, horizontal, adverse, critical).
(ii) The depth of flow relative to the normal depth ($y_n$) and critical depth ($y_c$).
- For a mild slope (M), we have: $y_c < y_n$ (critical depth is smaller than normal depth).

Step 2: Case of supercritical flow entering mild slope.
- Supercritical flow means actual depth of flow $y < y_c$. - Since $y < y_c < y_n$, the depth is below the critical depth region. - By GVF profile classification, this corresponds to M$_3$ profile.

Step 3: Verification.
- M$_1$: Depth $> y_n$ (not possible here).
- M$_2$: Depth between $y_c$ and $y_n$ (not possible since $y < y_c$).
- M$_3$: Depth $< y_c$ (true in case of supercritical flow).
\[ \boxed{\text{The flow profile becomes M$_3$.}} \]