Name: calculating trapezoidal channel flow rate
Uploaded: 2025-03-26T15:04:16.000Z
Duration: 1 min 18 s
Channel: JoVE

Consider a trapezoidal channel where water flows steadily at a certain depth, with a specified bottom width and side slopes angled to form the channel's cross-section.The channel bottom has a specified slope, which directly affects the flow velocity.Using these parameters, the goal is to calculate the flow rate for this channel configuration.The calculation begins by determining the cross-sectional area, combining contributions from the bottom width and the sloped side sections.Next, the wetted perimeter, consisting of both the bottom and side surfaces in contact with water, is calculated.Using these values, the hydraulic radius is obtained by dividing the cross-sectional area by the wetted perimeter.The Manning resistance coefficient, n, is selected for finished concrete lining to account for surface roughness.The hydraulic radius, together with the channel slope and other parameters, is substituted into Manning's equation.After the calculations, the flow rate is determined, representing the volume of water passing through the channel per unit of time.

uniform depth channel flow: problem solving

To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (&#952;) is determined by:<figure class="image image-style-align-center image_resized" style="display:table;margin-left:auto;margin-right:auto;width:12.94%;"><img style="aspect-ratio:524/154;" src="https://cloudfront.jove.com/files/ftp_upload/18094/18094_Equation_1_1__editor_18094.svg" alt="Equation of static equilibrium, A=yB+y(y/tan&#952;), mathematical formula analysis." data-altupdatedat="1762173717000" data-alt="18094_Equation_1_1_.svg" /></figure>Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by dividing the area by the perimeter. Select an appropriate Manning&#8217;s roughness coefficient based on the surface material of the channel. Apply Manning&#8217;s equation by substituting the hydraulic radius, channel slope, and roughness coefficient to find the flow velocity. Finally, calculate the flow rate by multiplying the flow velocity with the cross-sectional area. Always use consistent units throughout the process.

Uniform Depth Channel Flow: Problem Solving

To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional ...

uniform-depth-channel-flow-problem-solving

Education

JoVE Core

Civil Engineering

Unit 1

Open Channel Flow

KEY TERMS AND CONCEPTS

calculating trapezoidal channel flow rate

Calculating trapezoidal channel flow rate starts with the channel shape and the depth of flow. For a trapezoidal channel, identify the bottom width, side slope, and flow depth first. These values define the cross-section used in the calculation.

Next, find the cross-sectional area for the flowing water. Use the depth of flow, the bottom width, and the side slope angle to determine area. Then calculate the wetted perimeter, which includes the bottom width and the sloped side lengths that touch the water.

With area and wetted perimeter, determine the hydraulic radius by dividing area by perimeter. Select a Manning's roughness coefficient that matches the channel surface material. Then apply Manning's equation, using the hydraulic radius, channel slope, and roughness coefficient, to find flow velocity. Finally, multiply velocity by cross-sectional area to get the flow rate. Keep the units consistent throughout the process.

Calculating Trapezoidal Channel Flow Rate

calculating-trapezoidal-channel-flow-rate

energy considerations in open channel flow

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Flow Depth and Energy in Open Channels

Open channel flow involves water moving with a free surface exposed to the air. Rivers, canals, and artificial channels are common examples. In these systems, gravity and surface effects shape the flow more than the behavior seen in closed pipes. Energy analysis helps explain how depth, velocity, and slope work together. Specific energy combines the potential energy from water depth and the kinetic energy from flow speed. For a given discharge, or flow rate, there are often two possible depths...

uniform depth channel flow

Channel Slope and Flow Balance

Uniform depth channel flow keeps the water depth steady along an open channel. This idea is often used for irrigation canals and is also a useful approximation for rivers. The channel bottom slope must match the energy slope. That balance offsets the gravity energy lost to shear stress at the boundary, so the depth does not change along the channel length. In a constant cross-section channel, uniform flow means the depth and velocity stay consistent. Two key measures are the flow area and the...

Calculating trapezoidal channel flow rate starts with the channel shape and the depth of flow. For a trapezoidal channel, identify the bottom width, side slope, and flow depth first. These values define the cross-section used in the calculation. Next, find the cross-sectional area for the flowing water. Use the depth of flow, the bottom width, and the side slope angle to determine area. Then calculate the wetted perimeter, which includes the bottom width and the sloped side lengths that touch...

gradually varying flow

Open Channel Depth Changes in GVF

Gradually varying flow in open channels describes water depth that changes slowly along a channel. The depth adjusts over distance as gravity, shear forces, and energy needs stay in balance. This creates a low rate of change in the water surface. Gradually varying flow is common in natural streams, rivers, and canals. In these settings, the depth shifts little by little over long distances. The slope of the channel bed, compared with the energy slope, helps determine how the flow behaves. A...

 rapidly varying flow

Hydraulic Jumps in Open Channels

Rapidly varying flow in open channels describes a sudden change in water depth over a short distance. The depth can change so quickly that the rate of change with distance is close to one. These flows are difficult to analyze exactly because they are transient and multi-dimensional. Approximate solutions with simplified models still give useful insight into how they behave. A common example is the hydraulic jump. In a hydraulic jump, fast and shallow water changes quickly into slower, deeper...

hydraulic jump

Flow Regimes and Energy in Hydraulic Jumps

Hydraulic jumps happen in open channels when fast, shallow water changes into slower, deeper water. This sudden rise in depth depends on the upstream Froude number, which compares flow speed to wave speed. A hydraulic jump can form only when the upstream flow is supercritical, with Fr greater than 1. If Fr is less than 1, the flow is already subcritical, and a jump cannot form. That is because the jump would require a negative head loss, which is not possible under thermodynamic principles.

hydraulic jump: problem solving

Hydraulic Jump in a Rectangular Channel

Hydraulic jump in a rectangular channel shows how flow speed and water depth change when a gate closes downstream. The jump travels upstream at 2 meters per second, so that wave speed is part of the calculation. The initial channel flow speed is 6 meters per second. To find the water depths on each side of the jump, first calculate the effective upstream velocity. This combines the flow moving through the channel with the upstream-moving wave. Next, identify the flow velocities before and...

weir

Weir Flow Measurement and Control

A weir is a hydraulic structure that partly blocks an open channel and helps control water flow. It also makes it possible to measure discharge, which is the amount of water moving past a point in a given time. Because of this, weirs are important in water resource management. Weirs are used in river flow regulation, irrigation systems, and flood control channels. They guide water to flow over or through the structure, which lets engineers estimate flow rates more accurately. This makes them...

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Weir Flow Rates and Channel Depth

Weirs are hydraulic structures used to measure water flow in open channels. In a rectangular channel, they help calculate discharge, or the volume of water passing a point each second. The weir head is held at a fixed height above the channel bottom, which makes the math easier and lets students compare depth with flow rate. Three weir types are used in this setting: rectangular sharp-crested, triangular sharp-crested, and broad-crested. The rectangular sharp-crested weir depends on the weir...

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Irrigation Canal Gate Flow Control

Underflow gates control water flow in irrigation canals. They help manage discharge so water moves where and when it is needed. The main underflow gate types are vertical gates, radial gates, and drum gates. Vertical gates move up and down. They create a free-flowing water jet. Radial gates pivot to regulate flow, and drum gates rotate for fine adjustments. Each design supports effective flow management in different canal settings. Downstream conditions change how water passes through an...

design example: design of an irrigation channel

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Designing Trapezoidal Irrigation Channels

Trapezoidal irrigation channels are a common choice for moving water in farms and other water systems. Their flat bottom and sloping sides make them stable and easier to build than many other channel shapes. They are also cost-effective and efficient for carrying water. The channel size depends on the needed flow capacity and the site conditions. Designers choose the bottom width and the side slope ratio to match those demands. For unlined channels, the side slope is kept gentle to help...

key terms and concepts

Learn how to calculate trapezoidal channel flow rate using channel depth, wetted perimeter, hydraulic radius, and Manning’s equation with consistent units.

Calculating Trapezoidal Channel Flow Rate | JoVE K12

JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Calculating Trapezoidal Channel Flow Rate

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