Name: wind turbine torque and angular momentum
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 9 s
Channel: JoVE

تحلل معادلة لحظة الزخم عزم الدوران الناتج عن الشفرات الدوارة لتوربينات الرياح.
يتم العثور على معادلة عزم الزخم من خلال تطبيق قانون نيوتن الثاني على جسيم سائل صغير. ينص هذا القانون على أن معدل تغير الزخم الخطي يساوي القوة الخارجية المؤثرة عليه.
يتم حساب لحظة القوة من خلال النظر في موضع جسيم السائل لتحديد عزم الدوران.
يتم دمج متجه الموضع مع القوة الخارجية لإيجاد عزم الدوران المؤثر على الجسيم.
ثم يتم توسيع مشتق الوقت إلى جزأين. يمثل جزء واحد معدل تغير الزخم الزاوي بسبب سرعة السائل ، بينما يمثل الجزء الآخر كيفية تحرك السائل عبر الفضاء.
التغيير في الموضع بمرور الوقت يساوي سرعة الجسيم ، مما يبسط التمدد.
يتم الحصول على معادلة لحظة الزخم من خلال دمج هذه الحدود على حجم التحكم.
تربط هذه المعادلة عزم الدوران على النظام بالزخم الزاوي الذي يدخل ويخرج من حجم التحكم والقوى الخارجية المؤثرة عليه.

معادلة عزم الدوران.

<div style="direction:rtl">تعتبر معادلة عزم الزخم أداة بالغة الأهمية لتحليل القوى الدورانية الناتجة عن الريش الدوارة لتوربينات الرياح. يتم استنباط هذه المعادلة من خلال تطبيق قانون نيوتن الثاني على جسيم مائع، والذي ينص على أن معدل تغير الزخم الخطي يساوي القوة الخارجية المؤثرة على الجسيم. <img alt="Equation 1" src="/files/ftp_upload/18053/18053_Equation_1.svg" style="text-align: center; height: 48px;"> في حالة الأنظمة الدوارة مثل توربينات الرياح، يتم تحديد عزم هذه القوة، أو عزم الدوران، من خلال الاخذ في الاعتبار موضع الجسيم المائع بالنسبة لمحور الدوران. لحساب عزم الزخم، يتم الربط بين متجه موضع جسيم المائع والقوة الخارجية المؤثرة عليه. ينشأ عن هذا الربط عزم الدوران الذي يقوم الجسيم بتوليده. <img alt="Equation 2" src="/files/ftp_upload/18053/18053_Equation_2.svg" style="text-align: center; height: 52px;"> تتضمن الخطوة التالية توسيع المشتق الزمني لعزم الزخم. ينقسم هذا التوسيع إلى قسمين: أحدهما يمثل معدل تغير الزخم الزاوي الناتج عن سرعة الجسيم، والآخر يمثل حركة المائع عبر الفراغ. <img alt="Equation 3" src="/files/ftp_upload/18053/18053_Equation_3.svg" style="text-align: center; height: 96px;"> نظرًا لأن التغير في الموضع بمرور الوقت يساوي سرعة الجسيم، فإن التوسع الحسابي يصبح أبسط، مما يؤدي إلى فهم أوضح لكيفية عمل القوى داخل النظام الدوار. يتم الحصول على الشكل النهائي لمعادلة عزم الزخم من خلال دمج المعاملات ذات الصلة على حيز الدراسة، والذي يشمل منطقة المائع المتفاعل مع التوربين. <img alt="Equation 4" src="/files/ftp_upload/18053/18053_Equation_4.svg" style="text-align: center; height: 62px;"> توفر هذه المعادلة علاقة بين عزم الدوران المطبق على النظام والزخم الزاوي الداخل والخارج خلال حيز الدراسة، بالإضافة إلى القوى الخارجية المؤثرة على النظام. بالنسبة لتوربينات الرياح، يسمح هذا بإجراء تحليل مفصل لكيفية توليد الريش للطاقة الدورانية من الرياح، مما يؤدي إلى تحسين كفاءة وأداء التوربين.</div>

تحلل معادلة لحظة الزخم عزم الدوران الناتج عن الشفرات الدوارة لتوربينات الرياح.
تم العثور على معادلة لحظة الزخم بواسطة ...

Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Finite Control Volume Analysis

تحليل حجم التحكم المحدود

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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.

The next step is to expand the time derivative of the moment of momentum. One part describes the change in angular momentum caused by the particle's own velocity. The other part accounts for the fluid moving through space.

Because the change in position over time equals the particle's velocity, the expression simplifies. The final form is found by integrating over the control volume, which is the region of fluid that interacts with the turbine. This relationship connects torque with the angular momentum entering and leaving the control volume and with the external forces acting on the system.

For wind turbines, this equation helps show how the blades turn wind energy into rotational energy. It also supports more detailed analysis of turbine performance. That makes it useful for improving efficiency and understanding how the blades work.

Wind Turbine Torque and Angular Momentum

conservation of mass in finite cotrol volume

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

Continuity Equation for a Fixed Control Volume

The continuity equation describes conservation of mass for a fixed control volume. In fluid mechanics, a system is a collection of the same contents over time, and its mass stays constant. That idea is the starting point for deriving the equation. To analyze flow, a fixed, non-deforming control volume is chosen so it matches the system at one instant. The Reynolds transport theorem then links the system to the control volume. It shows that the rate of change of system mass has two parts: mass...

conservation of mass in fixed, nondeforming control volume

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

Continuity and Velocity in Pipe Flow

Conservation of mass explains how fluid moves through a fixed control volume such as a pipe or duct. In a fixed, nondeforming control volume, the total mass stays constant unless mass enters or leaves through the control surfaces. For steady, incompressible flow, the mass entering the system equals the mass leaving it. A sewer pipe is a useful example of this idea. It can be treated as a fixed control volume with inlet and outlet control surfaces around the flow region. Because the fluid is...

conservation of mass in moving, nondeforming control volume

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

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...

linear momentum in control volume

Momentum Balance for Fluid Control Volumes

Linear momentum balance for a fluid control volume links Newton’s second law to moving fluid. The law says that the rate of change of linear momentum equals the sum of the external forces acting on the system. In a fluid system, this idea helps explain how motion and force are related. A control volume can match the fluid system at a specific moment. When that happens, the forces on the control volume and the system are the same. Reynolds transport theorem explains this connection by splitting...

application of the linear momentum equation

application-of-the-linear-momentum-equation

Forces in a 180° Pipe Bend

Forces in a 180-degree pipe bend can be found by applying the linear momentum equation to flowing water. The pipe has a constant cross-sectional area of 0.01 square meters, and the water moves at 15 meters per second. The pressure at the inlet is 0.2 megapascals, and the pressure at the outlet is 0.16 megapascals. The goal is to find the force components in the x and y directions that hold the bend in place. In this case, the flow is only in the y direction at both the entrance and the exit.

moment-of-momentum equation

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...

application of the energy equation

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...

design example: forces in sluice gate

Sluice Gate Water Pressure and Reaction Force

Sluice gates control water flow in channels, reservoirs, and irrigation systems. They work as vertical barriers with an opening that can be raised or lowered. Changing the opening height changes the water velocity and pressure below the gate. The forces on a sluice gate depend on the water depths upstream and downstream, written as z1 and z2. When the gate is closed, the upstream water depth is greater. That creates a strong pressure difference across the gate and a net force toward the...

key terms and concepts

Learn how the moment-of-momentum equation links wind turbine torque, angular momentum, and control volume forces in rotating fluid systems for high school science.

Wind Turbine Torque and Angular Momentum | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Wind Turbine Torque and Angular Momentum

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