Types of Flow in Open Channels

Depending upon the change in depth of the fl ow with respect to space and time, open channel flows can be classified as follows.

1. Steady and unsteady flow

When the discharge rate is constant, the flow is a steady flow. The sectional areas at diff erent sections may be different. So mean velocity of fl ow at diff erent sections may also be diff erent

2. Uniform and non-uniform or varied flow

When depth of flow is same at all sections, the flow is a uniform flow. This means that velocity is same at all sections. Water surface is parallel to bed in this case. In a non-uniform flow, depth of section and mean velocity is different at different sections. Water surface is not parallel to bed in non-uniform flows.
A non-uniform or varied flow can be:
1. Rapidly varied flow (RVF)
2. Gradually varied flow (GVF)

3. Laminar flow and turbulent flow

The laminar motion of fluid is characterised by the motion in layers (i.e., laminar), parallel to the boundary surface.
The conditions favourable for laminar flow are:
1. High viscocity (m)
2. Low mass density (r)
3. Low mean velocity (V)
4. Small flow passage (L)

4. Subcritical flow, critical flow and super critical flow

Critical flow

It is defined as the flow at which specific energy is minimum or the flow corresponding to critical depth is defined as critical flow.
Relation of critical velocity with critical depth is: `v = (gh)^(1/2)
Froude number is 1 for critical flow.

Tranquil flow or streaming flow or sub-critical flow

When the depth of a flow in a channel is greater than critical depth (hc), the flow is said to be sub-critical flow.
Froude number is less than 1 for sub-critical flow.

Torrential flow or shooting flow or super-critical flow

When the depth of a flow in a channel is less than critical depth (hc), the flow is said to be sub-critical flow.
Froude number is greater than 1 for sub-critical flow.

Also It can be categorized into various types based on different parameters such as flow velocity, depth, roughness of the channel bed, and characteristics of the fluid. Some of the common types of flow in open channels include:

Uniform Flow:
In uniform flow, the flow velocity, depth, and other flow properties remain constant along the channel reach. This type of flow occurs when the slope of the channel, the roughness of the bed and banks, and the discharge remain constant. Uniform flow is often observed in long, straight channels with constant cross-sectional shape.
Non-Uniform Flow:
Non-uniform flow occurs when the flow properties vary along the channel, typically due to changes in channel slope, cross-sectional shape, or hydraulic characteristics. This type of flow is common in natural channels where there are variations in bed roughness, channel geometry, or where there are hydraulic structures such as bends, constrictions, or expansions.
Steady Flow:
Steady flow refers to a condition where the flow properties at any point in the channel remain constant over time. The flow rate, velocity, depth, and other parameters do not change with time. Steady flow can occur in both uniform and non-uniform flow conditions.
Unsteady Flow:
Unsteady flow occurs when the flow properties change with time at a particular point in the channel. This can happen due to sudden changes in discharge, channel geometry, or other hydraulic conditions. Unsteady flow is often observed during flood events, rapid changes in upstream flow rates, or when hydraulic structures are operated.
Critical Flow:
Critical flow occurs when the flow velocity equals the wave celerity, resulting in specific flow conditions known as critical depth. At critical flow conditions, small disturbances in flow depth or velocity can propagate upstream or downstream without any change in their amplitude. Critical flow is important in the design and analysis of hydraulic structures such as spillways and culverts.
Subcritical Flow:
Subcritical flow occurs when the flow velocity is less than the wave celerity, leading to gradually varying flow profiles downstream. In subcritical flow, disturbances propagate upstream, and flow properties change gradually along the channel. Most natural river flows are subcritical.
Supercritical Flow:
Supercritical flow occurs when the flow velocity exceeds the wave celerity, resulting in rapidly varying flow profiles downstream. In supercritical flow, disturbances propagate downstream, and flow properties change rapidly along the channel. Supercritical flow is often observed in steep channels, hydraulic jumps, and in high-velocity flow situations.

These are some of the fundamental types of flow in open channels related to soil and fluid mechanics. Understanding these flow types is essential for various engineering applications, including the design of drainage systems, irrigation canals, river management, and flood control structures.

Each type of flow with some examples to illustrate their characteristics:

Uniform Flow:
Imagine a straight canal with a constant slope, width, and depth. If the flow rate (discharge) remains constant and there are no changes in the channel's cross-sectional shape or roughness, the flow properties (velocity, depth) will also remain constant along the length of the canal. This is an example of uniform flow. It's like water flowing steadily through a long, straight pipe at a constant rate.
Non-Uniform Flow:
Consider a river that encounters a meander or a bend. As the river flows through the bend, the velocity and depth of the flow change. Near the outer bank of the bend, the flow is faster and deeper, while near the inner bank, the flow is slower and shallower. This variation in flow properties along the channel represents non-uniform flow. Another example could be a sudden constriction or widening of the channel, causing changes in flow properties.
Steady Flow:
Think of a canal with water flowing steadily through it. The flow rate, velocity, and depth at any given point in the canal remain constant over time. As long as there are no sudden changes in the channel or upstream conditions, the flow properties do not fluctuate. This represents steady flow. It's like a faucet with a constant stream of water flowing out.
Unsteady Flow:
Imagine a dam releasing water into a river at a variable rate over time. As the flow rate from the dam changes, the flow properties downstream of the dam also change. This fluctuation in flow properties with time represents unsteady flow. Another example could be a sudden flood event causing rapid changes in flow rates and depths in a river.
Critical Flow:
Consider water flowing through a narrow channel at a certain velocity. If the flow velocity reaches a critical value, known as critical velocity, the flow becomes critical. At this critical velocity, the depth of flow reaches a specific value known as critical depth, and the flow properties exhibit unique characteristics. An example of critical flow is when water flows through a hydraulic jump, such as at the base of a spillway.
Subcritical Flow:
Imagine water flowing gradually downstream in a river with a velocity slower than the wave celerity. In subcritical flow, small disturbances in flow propagate upstream, and the flow properties change gradually along the channel. This is typical of most natural river flows.
Supercritical Flow:
Consider water flowing rapidly downstream in a steep channel with a velocity greater than the wave celerity. In supercritical flow, disturbances propagate downstream, and the flow properties change rapidly along the channel. An example of supercritical flow is the flow downstream of a hydraulic jump, where the flow abruptly changes from subcritical to supercritical.

These examples should help you grasp the concept of different types of flow in open channels and how they relate to soil and fluid mechanics

Open channel

An open channel is a conduit through which fluid flows with a free surface exposed to the atmosphere. Unlike a closed conduit, such as a pipe, which contains the fluid within its boundaries, an open channel allows the fluid to flow freely along an open path. Here's a more detailed description:

Fluid Flow:
An open channel typically carries liquids such as water, although it can also carry other fluids like oil or sewage. The flow can be driven by gravity, pressure differences, or other forces.
Free Surface:
One distinguishing feature of an open channel is that the surface of the fluid is open to the atmosphere. This means that the top surface of the flowing liquid is exposed to air, allowing interactions such as evaporation and gas exchange to occur.
Channel Geometry:
Open channels can have various shapes and sizes, including natural formations such as rivers and streams, as well as man-made structures like canals and flumes. The geometry of the channel, including its width, depth, and cross-sectional shape, influences the behavior of the flowing fluid.
Boundary Conditions:
Unlike closed conduits where the fluid is confined within solid boundaries, open channels have boundary conditions determined by the interaction of the fluid with the channel bed and banks. Factors such as bed roughness, bank slope, and vegetation can affect the flow characteristics.
Hydraulic Considerations:
The study of open-channel flow involves analyzing the behavior of fluids in these open conduits. Engineers and scientists use principles from fluid mechanics, hydraulics, and sediment transport to understand and predict the behavior of open-channel flows.

Examples of open channels include:

Rivers and streams: Natural watercourses that flow along the Earth's surface.
Canals: Artificial waterways constructed for irrigation, navigation, drainage, or flood control purposes.
Ditches: Small channels dug to drain water from fields or convey runoff.
Flumes: Structures designed to measure the flow rate of water in open channels.
Culverts: Structures that allow water to flow beneath roads, railways, or embankments.

Understanding open-channel flow is essential in various engineering and environmental applications, including water resource management, flood forecasting, hydraulic structure design, and environmental protection.

Importance of flow in Engineering study

Different types of flow in open channels have varying levels of importance and utility in engineering applications, depending on the specific requirements and objectives of the project. Here's a breakdown of how each type of flow is commonly used in engineering:

Uniform Flow:
- Usefulness: Uniform flow is often desirable in engineering applications where a steady, predictable flow rate is required, such as in irrigation canals, water supply systems, and open-channel drainage networks.
- Example Application: Designing irrigation systems for agricultural fields often requires maintaining a constant flow rate to ensure uniform water distribution.
Non-Uniform Flow:
- Usefulness: Non-uniform flow is prevalent in natural watercourses and can also be engineered to achieve specific objectives, such as mitigating erosion or controlling sediment transport.
- Example Application: Designing riverbank protection measures to prevent erosion may involve considering non-uniform flow patterns near bends or constrictions.
Steady Flow:
- Usefulness: Steady flow conditions are essential for many engineering analyses and designs, providing a basis for hydraulic calculations and stability assessments.
- Example Application: Designing hydraulic structures like weirs or culverts often relies on steady flow assumptions to predict water levels, velocities, and pressure distributions.
Unsteady Flow:
- Usefulness: Unsteady flow analysis is crucial for predicting and managing flood events, analyzing transient phenomena, and designing hydraulic structures subjected to variable flow conditions.
- Example Application: Flood forecasting and emergency management systems use unsteady flow modeling to predict river behavior during storm events and develop evacuation plans.
Critical Flow:
- Usefulness: Critical flow conditions are important in hydraulic engineering for understanding hydraulic jumps, designing spillways, and analyzing flow transitions.
- Example Application: Designing spillways for dams involves ensuring that flow rates can be safely discharged without causing damage or erosion, which often requires consideration of critical flow conditions.
Subcritical Flow:
- Usefulness: Subcritical flow is commonly encountered in natural watercourses and is relevant for various engineering applications, such as river habitat restoration, sediment transport modeling, and ecosystem management.
- Example Application: Designing fish passages or habitat enhancements in rivers requires understanding how subcritical flow conditions affect water velocities and habitat suitability.
Supercritical Flow:
- Usefulness: Supercritical flow conditions are essential for analyzing hydraulic jumps, designing high-speed channels, and optimizing energy dissipation in hydraulic structures.
- Example Application: Designing energy dissipators for high-velocity flows in spillways or diversion channels involves optimizing flow conditions to prevent erosion and minimize turbulence.

In summary, each type of flow in open channels serves specific engineering purposes and is selected based on the project's objectives, constraints, and hydraulic considerations. Understanding the characteristics and applications of different flow types is essential for designing efficient and resilient hydraulic systems and structures.

Importance of Critical Flow study in Spillway design:

Critical flow conditions play a crucial role in the design and operation of spillways for dams. Spillways are hydraulic structures built to safely discharge excess water from a reservoir during periods of high inflow or flood events. Ensuring that flow rates can be safely discharged without causing damage or erosion is a primary concern in spillway design, and critical flow conditions are fundamental to achieving this objective. Here's a more detailed explanation of how critical flow considerations are relevant in spillway design:

Hydraulic Jump Formation: One of the key aspects of spillway design is managing the energy dissipation of the discharged flow to prevent erosion and downstream scour. When high-velocity flow discharges from a spillway into a lower-energy environment, such as a downstream channel or riverbed, a hydraulic jump typically forms. A hydraulic jump is a phenomenon where the flow transitions from supercritical to subcritical, resulting in rapid energy dissipation and turbulence. Critical flow conditions are crucial in determining the characteristics and stability of the hydraulic jump.
Energy Dissipation: Critical flow conditions are associated with the formation and stability of hydraulic jumps, which play a critical role in dissipating the excess energy of the discharged flow. By promoting the formation of hydraulic jumps, spillway designers can effectively dissipate the kinetic energy of the flowing water, reducing its erosive potential and minimizing downstream impacts such as scour and erosion.
Chute and Stilling Basin Design: Spillway structures often include features such as chutes and stilling basins, which are designed to facilitate the formation and stabilization of hydraulic jumps. Chutes are sloped sections that accelerate the flow, while stilling basins are typically flat or gradually sloping areas where the hydraulic jump occurs and energy dissipation takes place. Critical flow considerations inform the design of these structures to ensure that hydraulic jumps form reliably and safely under a range of flow conditions.
Flow Capacity and Discharge Efficiency: Critical flow conditions also influence the capacity and efficiency of spillways in discharging flow from the reservoir. By optimizing the design to promote critical flow and hydraulic jump formation, engineers can maximize the flow capacity of the spillway while minimizing the risk of erosion and damage downstream. This allows for the safe and effective management of flood events and reservoir operations.

In summary, critical flow considerations are essential in spillway design for dams to ensure the safe and efficient discharge of excess water while minimizing erosion and downstream impacts. By understanding and leveraging critical flow conditions, engineers can design spillways that effectively dissipate energy, prevent damage, and protect downstream communities and infrastructure during flood events.

Froude number and Critical Flow

The Froude number` (\(Fr\))` indeed plays a crucial role in determining critical flow conditions in open-channel flow. When the Froude number is unity `(\(Fr = 1\))` at a certain depth of flow, it indicates critical flow conditions. This critical flow condition is characterized by the flow velocity being equal to the wave celerity, resulting in a balanced relationship between gravitational and inertial forces. At this point, the flow is said to be at critical velocity, and the depth at which this occurs is referred to as the critical depth `(\(y_c\))`.

The Froude number is defined as the ratio of flow velocity to the square root of the product of gravity and flow depth:

`\[ Fr = \frac{V}{\sqrt{g \cdot y}} \]`

Where:
- `\( V \)` = Flow velocity
- `\( g \)` = Acceleration due to gravity
- `\( y \)` = Flow depth

When` \( Fr = 1 \)`, it signifies that the flow velocity is critical, meaning that the flow velocity is just sufficient to overcome the gravitational forces acting on the flow, resulting in critical flow conditions.

In summary, the Froude number being unity at a specific depth indicates critical flow conditions, where the flow velocity equals the wave celerity, and this depth is known as the critical depth. Thank you for pointing out the connection between Froude number, critical velocity, and critical depth in open-channel flow.

The concepts of subcritical, critical, and supercritical flow in open-channel hydraulics, along with explanations of celerity and energy:

1. Subcritical Flow:
- Definition:

Subcritical flow occurs when the flow velocity `(\(V\))` is less than the wave celerity `(\(C\))`, resulting in a Froude number `(\(Fr\))` less than 1 `(\(Fr < 1\))`.

- Characteristics:

In subcritical flow, the flow depth `(\(y\))` is relatively deep compared to the wavelength, and gravitational forces dominate inertial forces. Waves propagate upstream in subcritical flow, and disturbances in flow properties gradually attenuate.

- Froude Number Relationship:

`\(Fr < 1\)`

- Example:

Steady flow in a natural river channel with moderate velocity, where the flow depth is greater than the critical depth.

2. Critical Flow:
- Definition:

Critical flow occurs when the flow velocity (\(V\)) equals the wave celerity (\(C\)), resulting in a Froude number (\(Fr\)) equal to 1 (\(Fr = 1\)).

- Characteristics:

At critical flow conditions, gravitational and inertial forces are in balance, and waves neither advance nor retreat. Critical flow often occurs at critical depth (\(y_c\)).

- Froude Number Relationship:

`\(Fr = 1\)`

- Example:

Hydraulic jump in a spillway, where the flow velocity transitions from supercritical to subcritical.

3. Supercritical Flow:
- Definition:

Supercritical flow occurs when the flow velocity `(\(V\))` exceeds the wave celerity `(\(C\))`, resulting in a Froude number `(\(Fr\))` greater than 1 `(\(Fr > 1\))`.

- Characteristics:

In supercritical flow, the flow depth `(\(y\))` is relatively shallow compared to the wavelength, and inertial forces dominate gravitational forces. Waves propagate downstream in supercritical flow, and disturbances in flow properties rapidly amplify.

- Froude Number Relationship:

`\(Fr > 1\)`
- Example:

Rapid flow over a hydraulic jump, where the flow velocity is high, and the flow depth is shallow.

Celerity:

Celerity `(\(C\))` refers to the speed at which waves or disturbances propagate through a fluid medium. In the context of open-channel flow, wave celerity is the speed at which small disturbances in flow properties (such as depth or velocity) travel along the flow direction. It is calculated as the square root of the product of gravity `(\(g\))` and the flow depth `(\(y\))` for steady, uniform flow:

`\[ C = \sqrt{g \cdot y} \]`

Energy in Open-Channel Flow:
The energy associated with open-channel flow consists of two components:
- Kinetic Energy:

This is the energy associated with the flow velocity `(\(V\))`. It represents the energy per unit weight of fluid due to the motion of the fluid particles.

- Potential Energy:

This is the energy associated with the elevation of the flow. It represents the energy per unit weight of fluid due to the gravitational force acting on the fluid.

The total energy per unit weight of fluid, also known as specific energy `(\(E\))`, is the sum of kinetic and potential energies:

`\[ E = \frac{V^2}{2} + g \cdot y \]`

Where:
- `\( E \)` = Specific energy
- `\( V \)` = Flow velocity
- `\( g \)` = Acceleration due to gravity
- `\( y \)` = Flow depth

In critical flow conditions, the specific energy is minimized, leading to the formation of a hydraulic jump where excess kinetic energy is dissipated as turbulence and potential energy increases.

Understanding the relationships between flow velocity, celerity, Froude number, and energy is crucial for analyzing and designing open-channel flow systems and hydraulic structures. These concepts are fundamental to hydraulic engineering and play a significant role in various applications, including flood management, river engineering, and water resource development.

Grade of Steel	X_u,lim/d
Fe 250	0.53
Fe 400	0.48
Fe 500	0.46

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CSE - Civil Engineering Study

Table of Contents

Limiting Moment of Resistance of a RCC Beam

The limiting Moment of Resistance of a RCC Beam is given as:

Development Length of Steel bar in RCC

Moisture Contents of Soil