Name: turbine work from energy changes
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

High School

Chemistry

Energy

C-PS3-4

Conservation of Energy in Control Volume

ينص القانون الأول للديناميكا الحرارية على أن معدل تغير إجمالي الطاقة المخزنة في النظام يساوي صافي معدل الحرارة والعمل المنقول إلى النظام.
بالنسبة لحجم التحكم الذي يتزامن مع النظام في لحظة معينة ، فإن صافي الحرارة والعمل الذي يدخل النظام يساوي صافي الحرارة والعمل الذي يدخل حجم التحكم.
بالنسبة لهذا النظام وحجم التحكم المتزامن ، يتم تطبيق نظرية نقل رينولدز.
يتم تحديد المعدل الإجمالي لتغير الطاقة داخل حجم التحكم من خلال كل من المعدل الزمني للتغيير في الطاقة المخزنة وصافي تدفق الطاقة عبر الحدود.
تشمل الطاقة المتدفقة عبر الحدود مساهمات من الحرارة والعمل ، مثل عمل العمود وعمل الضغط.
ينتج عمل العمود عن المكونات الدوارة مثل التوربينات ، بينما تنتج ضغوط السوائل عمل الضغط.
تجمع معادلة الطاقة العامة بين جميع العناصر: الطاقة المخزنة ، والحرارة ، وعمل العمود ، وعمل الضغط بسبب الضغوط العادية.
تمثل هذه المعادلة الحفاظ على الطاقة في أنظمة السوائل ، بما في ذلك نقل الحرارة ، وعمل العمود ، وقوى الضغط على سطح التحكم.

مبدأ بقاء الطاقة في حيز الدراسة

<div style="direction:rtl">لنفترض توربين يعمل تحت ظروف التدفق المستقر. يتم رسم حيز الدراسة حول التوربين، يدخل السائل عند نقطة واحدة ويخرج عند نقطة أخرى. يستخرج التوربين الطاقة من السائل، الذي يقوم بببذل شغل ميكانيكي (تحريك العمود). في أنظمة التدفق المستقر، يساوي المشتق الزمني للطاقة المخزنة صفرًا نظرًا لعدم تراكم الطاقة داخل حيز الدراسة. هذا يبسط معادلة الطاقة إلى: <img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;"> نظرًا لأننا نركز على العمل الذي يقوم به عمود التوربين ونفترض انتقال لايذكر للحرارة، لذا يتم تبسيط معادلة الطاقة إلى: <img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;"> يتم التعبير عن التدفق من خلال مكونين: السائل الذي يدخل التوربين (المدخل) والسائل الذي يخرج من التوربين (المخرج). معدل تدفق الكتلة عند كلتا النقطتين ثابت، ويتم تحديد تدفق الطاقة عند المدخل والمخرج بواسطة: <img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;"> حيث: -ṁ هو معدل تدفق الكتلة، - ũ1، V1، وz1 يشير إلى الطاقة الداخلية والسرعة والارتفاع عند المدخل، - ũ2، V2، وz2 يشير إلى الطاقة الداخلية والسرعة والارتفاع عند المخرج، في نماذج التوربينات المعتادة، تنخفض الطاقة الداخلية والحركية للسائل أثناء مروره عبر التوربين، مما يؤدي إلى بذل شغل مفيد على العمود. افترض أن التوربين يعمل بسرعة دخول V1 = 50 م/ث، وسرعة خروج V2 = 20 م/ث، وارتفاع دخول z1 مائة متر، وارتفاع خروج z2 تسعون متراً. بافتراض أن تغير الطاقة الداخلية صغير مقارنة بتغيرات الطاقة الحركية والكامنة، وأن معدل تدفق الكتلة <img style="text-align: center; height: 12px;" src="data:image/png;base64,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" /> هو 10 كجم/ث. <img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;"> نتيجة لذلك، ينتج التوربين ما يقرب من 11.48 كيلو وات من الطاقة الميكانيكية عن طريق توليد الطاقة من السائل المتدفق.</div>

ينص القانون الأول للديناميكا الحرارية على أن معدل تغير إجمالي الطاقة المخزنة في النظام يساوي المعدل الصافي للحرارة والعمل المنقول إلى ...

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

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 is then described by the mass flow rate and by the fluid’s internal energy, velocity, and height at each location.

For the inlet and outlet, the mass flow rate is constant. The energy flux depends on ṁ, u1, V1, and z1 at the inlet, and on ṁ, u2, V2, and z2 at the outlet. Here, u is internal energy, V is velocity, and z is height.

In a typical turbine, the fluid loses internal energy and kinetic energy as it moves through the device. That energy loss becomes useful shaft work. For example, if V1 = 50 m/s, V2 = 20 m/s, z1 = 100 m, z2 = 90 m, and the mass flow rate is 10 kg/s, with a small internal energy change, the turbine produces about 11.48 kW of mechanical power.

Turbine Work from Energy Changes

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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

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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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...

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Learn how a steady-flow turbine uses changes in velocity, height, and internal energy to produce shaft work, with a worked 11.48 kW example.

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Turbine Work from Energy Changes

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