Hydraulic Jump Calculation

Hydraulic Jump Depth Ratio:

\[ \frac{h_2}{h_1} = \frac{\sqrt{1 + 8 Fr_1^2} - 1}{2} \]

Downstream Depth (h₂):

Froude Number (Fr₁):

Depth Ratio (h₂/h₁):

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1. What is Hydraulic Jump?

A hydraulic jump is a phenomenon in fluid dynamics where a rapidly flowing liquid suddenly slows down, resulting in a rise in liquid surface level. It represents the transition from supercritical (Fr > 1) to subcritical (Fr < 1) flow.

2. How Does the Calculator Work?

The calculator uses the hydraulic jump depth ratio equation:

\[ \frac{h_2}{h_1} = \frac{\sqrt{1 + 8 Fr_1^2} - 1}{2} \]

Where:

\( h_1 \) — Upstream depth (m)
\( h_2 \) — Downstream depth (m)
\( Fr_1 \) — Upstream Froude number (\( v_1/\sqrt{g h_1} \))
\( v_1 \) — Upstream velocity (m/s)
\( g \) — Gravitational acceleration (9.81 m/s²)

Explanation: The equation relates the depth before and after the jump based on the Froude number of the upstream flow.

3. Importance of Hydraulic Jump Calculation

Details: Hydraulic jumps are important in engineering for energy dissipation in spillways, preventing erosion, mixing chemicals in water treatment, and maintaining water levels in canals.

4. Using the Calculator

Tips: Enter upstream depth in meters, upstream velocity in m/s. All values must be valid (depth > 0, velocity ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the Froude number?
A: The Froude number is a dimensionless number that characterizes flow regimes. Fr < 1 is subcritical (tranquil), Fr > 1 is supercritical (rapid), and Fr = 1 is critical flow.

Q2: When does a hydraulic jump occur?
A: A hydraulic jump occurs when a supercritical flow encounters a subcritical flow, forcing a sudden transition between the two flow regimes.

Q3: What is the energy loss in a hydraulic jump?
A: Significant energy is dissipated in a hydraulic jump, which can be calculated using the specific energy equation before and after the jump.

Q4: Are there different types of hydraulic jumps?
A: Yes, jumps are classified as undular (1 < Fr < 1.7), weak (1.7 < Fr < 2.5), oscillating (2.5 < Fr < 4.5), steady (4.5 < Fr < 9), and strong (Fr > 9).

Q5: Where are hydraulic jumps commonly observed?
A: Common in dam spillways, under sluice gates, in kitchen sinks when water hits flat surfaces, and in tidal bores.