A Hydraulic Jump is said to be Oscillating Jump if its Froude number is ________.
Between 2.5 to 4.5
A Hydraulic Jump is a phenomenon that occurs in open channel flow when supercritical flow transitions to subcritical flow. This transition is accompanied by a sudden rise in the liquid surface and significant energy dissipation, often observed as turbulence and air entrainment.
The behavior and characteristics of a Hydraulic Jump are largely dependent on the flow conditions upstream of the jump. These conditions are typically characterized by the Froude number.
Hydraulic Jump Froude Number Ranges
The Froude number (Fr) is a dimensionless parameter that represents the ratio of inertial forces to gravitational forces in a fluid flow. It is calculated as:
\[ Fr = \frac{V}{\sqrt{gy}} \]
Where:
- \(V\) is the mean flow velocity
- \(g\) is the acceleration due to gravity
- \(y\) is the flow depth
For open channel flow, if \(Fr > 1\), the flow is supercritical; if \(Fr < 1\), the flow is subcritical; and if \(Fr = 1\), the flow is critical.
The type and behavior of a hydraulic jump are classified based on the Froude number of the flow just upstream of the jump (\(Fr_1\)). Different ranges of \(Fr_1\) correspond to different types of hydraulic jumps:
- Weak Jump: Occurs when \(1 < Fr_1 < 1.7\). The jump is barely perceptible, with small surface undulations.
- Undular Jump: Occurs when \(1 < Fr_1 < 1.7\) (sometimes included with Weak Jump). A series of undulations appear on the surface.
- Oscillating Jump: Occurs when \(2.5 < Fr_1 < 4.5\). The jump oscillates back and forth, causing large waves that can propagate downstream for long distances, potentially damaging channel structures.
- Stable or Well-Balanced Jump: Occurs when \(4.5 < Fr_1 < 9\). This is the most stable and effective jump, with good energy dissipation.
- Strong or Choppy Jump: Occurs when \(Fr_1 > 9\). The jump is very rough and turbulent, with significant energy loss but can be less stable than the well-balanced jump.
Let's summarize these classifications in a table:
| Type of Hydraulic Jump | Upstream Froude Number (\(Fr_1\)) Range |
|---|---|
| Weak/Undular Jump | \(1 < Fr_1 < 1.7\) |
| Oscillating Jump | \(2.5 < Fr_1 < 4.5\) |
| Stable/Well-Balanced Jump | \(4.5 < Fr_1 < 9\) |
| Strong/Choppy Jump | \(Fr_1 > 9\) |
Based on the classification, a Hydraulic Jump is said to be an Oscillating Jump if its Froude number just upstream of the jump is between 2.5 and 4.5.
Important Questions from Open Channel Flow
- A trapezoidal channel carries $5\text{ m}^3\text{.s}^{-1}$ of water under uniform flow condition. The channel has a bottom width of $2\text{ m}$, side slope of $2:1$ (horizontal: vertical), and a bed slope of $1\%$. If the Manning roughness coefficient is $0.03$, the conveyance of the channel, in $\text{m}^3\text{.s}^{-1}$, is
- Two rectangular channels, A and B, join to form a large rectangular channel, C. Each rectangular channel is lined with the same material and has the same bottom slope. The bottom widths of Channels A and B are $2\text{ m}$ and $1\text{ m}$, respectively. If the flow depth in each channel is $2\text{ m}$, the bottom width of Channel C (in m) is ________. (Rounded off to two decimal places)
- Water is flowing at the rate of 15 m$^3$/s through a rectangular channel of 5 m width.
If the acceleration due to gravity ($g$) is 9.81 m/s$^2$, the critical velocity for the flow is ______ m/s (rounded off to three decimal places). The Francis formula for the discharge over cippoletti weir is
The Cippoleti weir is a ______ weir.
