Critical flow condition in open channels The flow in an open channel is termed “critical” when the Froude number Fr equals what value?
-
Aless than 1.0
-
Bequal to 1.0
-
Cgreater than 1.0
-
DNone of these
-
Eequal to 0.5
Answer
Correct Answer: equal to 1.0
Explanation
Introduction / Context:The Froude number Fr = V / √(g D_h) compares flow inertia to gravity effects (D_h is hydraulic depth). It classifies free-surface flows as subcritical, critical, or supercritical—vital for control structures, spillways, and rapidly varied flow predictions.
Given Data / Assumptions:
- Steady, one-dimensional open-channel flow.
- Hydraulic depth D_h = A / T (area over top width).
- Froude number Fr = V / √(g D_h).
Concept / Approach:
By definition, critical flow occurs when specific energy is minimized for a given discharge, and mathematically when Fr = 1. Subcritical flows have Fr < 1 (gravity-dominated), while supercritical flows have Fr > 1 (inertia-dominated).
Step-by-Step Solution:
Compute Fr from measured V and D_h.If Fr = 1 → critical; Fr < 1 → subcritical; Fr > 1 → supercritical.Design transitions (e.g., weirs, flumes) often target Fr ≈ 1 to create critical depth.Verification / Alternative check:
At critical conditions, specific energy E has a stationary point with respect to depth, consistent with GVF theory.
Why Other Options Are Wrong:
(a) and (c) correspond to subcritical and supercritical regimes; (d) and (e) contradict the definition.
Common Pitfalls:
Confusing hydraulic depth with hydraulic radius; using local depth in irregular sections without proper definition of D_h.
Final Answer:
equal to 1.0