Name: stormwater detention basin mass balance
Uploaded: 2025-02-13T15:43:21.000Z
Duration: 1 min 14 s
Channel: JoVE

The conservation of mass is crucial in understanding the water flow in a rotating sprinkler system used for agricultural irrigation.
The sprinkler receives water from a stationary source and ejects it through rotating nozzles to irrigate the field.
The control volume includes the water inside the sprinkler head and nozzles, with the boundaries defined by the nozzle openings and the water source inlet.
Water flows steadily through the system as the sprinkler rotates, maintaining a continuous irrigation pattern.
The water&#39;s relative velocity is determined by its speed as it exits the nozzle compared to the motion of the rotating sprinkler head.
The difference between the water&#39;s absolute velocity and the rotating sprinkler&#39;s velocity determines how fast the water is ejected relative to the moving nozzle.
For steady flow, the inflow of water from the source and the outflow through the nozzles must be balanced.
The nozzle size and rotation speed are designed to ensure uniform water distribution across the field and maximize irrigation efficiency.

conservation of mass in moving, nondeforming control volume

Conservation of Mass in Moving, Nondeforming Control Volume

Stormwater detention basins are essential in managing runoff during heavy rainfall, particularly in urban areas where impervious surfaces increase the risk of flooding. Understanding the conservation of mass in these systems allows engineers to optimize basin performance, balancing inflow, outflow, and water storage.
In the context of a detention basin, the conservation of mass states that the total mass of water entering the basin must equal the mass leaving the basin plus any accumulation of water within it. The control volume consists of the water inside the basin, with its boundaries defined by the basin walls, inflow pipes, and outflow structures. During a rainfall event, inflow occurs through the pipes, and outflow through the designed outlets. The mass balance equation is expressed as:
<img alt="Continuity equation in fluid dynamics; mass conservation formula; equation analysis." src="/files/ftp_upload/18050/18050_Equation_1.svg" style="text-align: center; height: 33px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Where
&#7745;in is the mass inflow rate,
&#7745;out is the mass outflow rate and
<img alt="Static equilibrium &#931;Fx=0 diagram showing force vectors for mechanical balance analysis." src="/files/ftp_upload/18050/18050_Equation_2.png" style="text-align: center; height: 33px;" data-altupdatedat="1762173717000" data-alt="Equation 1" /> represents the change in mass inside the control volume.
During heavy rainfall, the inflow rate often exceeds the outflow rate, causing water to accumulate in the basin. Engineers must design the outflow structures to control the release of water at a manageable rate, ensuring that downstream systems are not overwhelmed. As the storm subsides and the inflow decreases, the accumulated water is gradually released. The outflow rate is typically designed to increase as the water level rises, following predetermined discharge curves to maintain control over the release.
The detention basin's ability to temporarily store water is critical to flood prevention. Properly designed detention basins ensure that water is released in a controlled manner during even the most intense storm events, preventing overflow or structural failure.

The conservation of mass is crucial in understanding the water flow in a rotating sprinkler system used for agricultural irrigation.
The sprinkler ...

conservation-of-mass-in-moving-nondeforming-control-volume

Education

JoVE Core

Civil Engineering

Unit 1

Finite Control Volume Analysis

KEY TERMS AND CONCEPTS

stormwater detention basin mass balance

Stormwater detention basins use mass balance to manage runoff during heavy rainfall. These basins are especially important in urban areas, where impervious surfaces can increase flooding risk. Engineers use the conservation of mass to track how water enters, is stored in, and leaves the basin.

In a detention basin, the control volume is the water inside the basin. Its boundaries are the basin walls, the inflow pipes, and the outflow structures. During a rain event, water comes in through the pipes and exits through the outlet system.

The mass balance equation states that the mass flowing into the basin must equal the mass flowing out plus any water that builds up inside. Here, m-dot in is the mass inflow rate, m-dot out is the mass outflow rate, and the change in mass shows how much water is accumulating in the control volume. When heavy rain causes inflow to exceed outflow, water storage in the basin increases.

Engineers design the outlet structures to release water at a manageable rate so downstream systems are not overwhelmed. As the storm weakens and inflow drops, the stored water is released more slowly. The outflow rate is often designed to rise as the water level rises, following preset discharge curves. This controlled storage is what helps detention basins prevent overflow and structural failure during intense storms.

Stormwater Detention Basin Mass Balance

conservation of mass in finite cotrol volume

conservation-of-mass-in-finite-cotrol-volume

Continuity Equation for a Fixed Control Volume

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conservation of mass in fixed, nondeforming control volume

conservation-of-mass-in-fixed-nondeforming-control-volume

Continuity and Velocity in Pipe Flow

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Stormwater detention basins use mass balance to manage runoff during heavy rainfall. These basins are especially important in urban areas, where impervious surfaces can increase flooding risk. Engineers use the conservation of mass to track how water enters, is stored in, and leaves the basin. In a detention basin, the control volume is the water inside the basin. Its boundaries are the basin walls, the inflow pipes, and the outflow structures. During a rain event, water comes in through the...

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moment-of-momentum equation

Wind Turbine Torque and Angular Momentum

The moment-of-momentum equation helps explain how wind turbine blades create torque. Torque is the turning effect of a force around an axis. In rotating systems, this equation links the motion of the wind with the force acting on it. The equation begins with Newton's second law for a fluid particle. That law says the rate of change of linear momentum equals the external force on the particle. To find torque, the position of the particle relative to the rotation axis is combined with that force.

conservation of energy in control volume

Turbine Work from Energy Changes

A turbine can turn fluid energy into shaft work when flow passes through a control volume. The fluid enters the turbine at one point and leaves at another. Under steady-flow conditions, there is no energy buildup inside the control volume, so the stored energy does not change with time. This steady-flow setup makes the energy equation simpler. The turbine is treated as doing mechanical work, and heat transfer is taken as negligible, so Q̇ is approximately zero. The flow at the inlet and outlet...

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Centrifugal Pump Flow Rate Calculation

Centrifugal pump flow rate can be calculated with the energy equation. In this problem, water moves between two reservoirs at different elevations, and the pump provides the energy needed for the transfer. The pump input is 7500 joules per second, the elevation difference is 10 meters, and the head loss from friction and other resistances is 5 meters. Both reservoirs are open to the atmosphere, so the pressure at the inlet and outlet is the same. That means the pressure terms in the energy...

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Sluice Gate Water Pressure and Reaction Force

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key terms and concepts

See how stormwater detention basins use conservation of mass to balance inflow, outflow, and storage during heavy rain to reduce flooding.

Stormwater Detention Basin Mass Balance | 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.

Stormwater Detention Basin Mass Balance

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