Rule of thumb for hydraulic jump length For practical design estimates, the length of a hydraulic jump on a horizontal floor is approximately how many times the jump height?

Introduction / Context:Hydraulic jumps dissipate supercritical flow energy and stabilize downstream conditions. Designers need quick estimates of jump length for apron sizing and protection against scour.

Given Data / Assumptions:

• Horizontal, prismatic rectangular channel.
• Subcritical tailwater permitting a stable jump.
• Empirical rule for preliminary design (not a strict analytical derivation).

Concept / Approach:Experiments show that the roller length L_j correlates with the sequent-depth ratio and Froude number upstream. A robust field rule is L_j ≈ 5 to 7 times the jump height (difference between the sequent depths). This range covers common Froude numbers encountered in spillways and sluices.

Step-by-Step Solution:

Verification / Alternative check:Compare with design charts correlating L_j/Δy to Fr₁; for Fr₁ ≈ 2–6, values commonly lie in the 5–7 range.

Why Other Options Are Wrong:2–3 and 3–5 under-estimate the roller for many practical cases, risking inadequate apron length.

Common Pitfalls:Ignoring tailwater control; applying the rule uncritically to sloping or rapidly varying channels without adjustment.

Final Answer:5 to 7 times its height