Open-Channel Flow Classification – Depth vs Critical Depth If the actual flow depth in an open channel is greater than the critical depth, the regime is called subcritical (also termed tranquil) flow. This state is gravity-dominated with Froude number less than 1.

Introduction:
In open-channel hydraulics, flow is categorized by comparing the actual depth with the critical depth and, equivalently, by the Froude number Fr = V / sqrt(g * y_h). Recognizing subcritical (tranquil) versus supercritical (torrential) flow determines how disturbances propagate and which equations or control sections to use.

Given Data / Assumptions:

• Prismatic open channel carrying water under gravity.
• Depth is greater than the critical depth for the given discharge and section.
• Hydraulic depth y_h is characteristic depth (equals flow area divided by top width for general sections).

Concept / Approach:

Critical depth is defined where specific energy is minimum for a given discharge. When actual depth is larger than the critical depth, gravitational potential effects dominate inertial effects, yielding a low Froude number (Fr < 1) and tranquil behavior. Surface waves can travel upstream in subcritical flow, which is important for control and measurement.

Step-by-Step Solution:

Verification / Alternative check:

On a mild channel slope with given discharge, backwater curves (M-profiles) occur when depth exceeds normal or approaches subcritical conditions, consistent with tranquil flow characteristics (slow, deep, gravity-dominated).

Why Other Options Are Wrong:

Torrential flow: Another name for supercritical, requires Fr > 1 and depth less than critical. Critical flow: Occurs only at exactly the critical depth (Fr = 1). Supercritical flow and rapid flow: Both indicate depth less than critical with high velocity.

Common Pitfalls:

Confusing the terms tranquil and torrential; mixing pipe flow criteria (Reynolds number) with open-channel criteria (Froude number); assuming high depth always implies high discharge without considering section shape and specific energy.

Final Answer:

tranquil flow