The Cippoleti weir is a ______ weir.
Trapezoidal
A weir is a structure that is built across an open channel, like a river or canal, to measure the rate of flow of water or to raise the water level. Weirs are fundamental components in hydraulic engineering, used for managing water resources, irrigation, and flood control. Different types of weirs are distinguished by their shape and design, which in turn affect how discharge is calculated.
The question specifically asks about the type of weir known as the Cippoletti weir. Understanding its design is key to identifying its shape.
Cippoletti Weir Definition
The Cippoletti weir is a particular type of weir characterized by its unique shape, which is designed to provide a direct and simplified method for measuring water flow. Its most distinctive feature is its cross-sectional shape, which is not circular, rectangular, or triangular, but rather trapezoidal.
Trapezoidal Weir Design
A standard Cippoletti weir has a trapezoidal notch with side slopes. These side slopes are not arbitrary; they are specifically designed at a ratio of 1 horizontal to 4 vertical (1H:4V). The ingenious purpose of this specific slope is to automatically compensate for the effect of "end contractions." End contractions are the phenomena where the flowing water contracts laterally as it passes over the weir, effectively reducing the width of the flow. For a simple rectangular weir, these contractions can make discharge calculations more complex.
The trapezoidal shape of the Cippoletti weir ensures that the additional discharge gained from the flow over the two triangular side portions precisely balances the reduction in discharge caused by the two end contractions. This self-compensating feature simplifies the discharge formula, making it similar to that of a rectangular weir without any end contractions. This is a significant advantage in practical hydraulic measurements.
The discharge \(Q\) over a Cippoletti weir can be calculated using the formula:
$$Q = C_d \frac{2}{3} \sqrt{2g} B H^{3/2}$$
Where:
- \(Q\) is the discharge (volume per unit time)
- \(C_d\) is the coefficient of discharge (commonly taken as 0.63)
- \(g\) is the acceleration due to gravity (approximately \(9.81 \text{ m/s}^2\))
- \(B\) is the length of the weir crest (the bottom horizontal part of the trapezoid)
- \(H\) is the head of water over the weir (the vertical depth of water above the crest)
This formula demonstrates how the trapezoidal shape simplifies calculations by effectively eliminating the need to account for end contractions separately.
Weir Types Overview
To put the Cippoletti weir into context, here’s a brief comparison of common weir types:
| Weir Type | Shape Description | Key Characteristic/Application |
|---|---|---|
| Rectangular Weir | Rectangular notch | Common for general flow measurement; can have end contractions or be suppressed. |
| Triangular Weir (V-notch weir) | V-shaped notch | Ideal for measuring small discharges with high accuracy. |
| Trapezoidal Weir (Cippoletti) | Trapezoidal notch with specific side slopes (1H:4V) | Self-compensating for end contractions, simplifying discharge calculations. |
| Circular Weir | Circular opening | Less common in open channels, sometimes used in pipes or specific outlets. |
Given its unique design and specific side slopes to counter end contractions, the Cippoletti weir is classified as a trapezoidal weir.
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). A Hydraulic Jump is said to be Oscillating Jump if its Froude number is ________.
The Francis formula for the discharge over cippoletti weir is
