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

Termodinamiğin birinci yasası, bir sistemde depolanan toplam enerjinin değişim hızının, bir sisteme aktarılan net ısı ve iş oranına eşit olduğunu belirtir.
Belirli bir anda sistemle çakışan bir kontrol hacmi için, sisteme giren net ısı ve iş, kontrol hacmine giren net ısı ve işe eşittir.
Bu sistem ve çakışan kontrol hacmi için Reynolds Taşıma Teoremi uygulanır.
Kontrol hacmi içindeki toplam enerji değişim hızı, hem depolanan enerjideki değişimin zaman oranı hem de sınırdan geçen net enerji akışı ile belirlenir.
Sınır boyunca akan enerji, şaft işi ve basınç işi gibi ısı ve işten gelen katkıları içerir.
Şaft işi, türbinler gibi dönen bileşenlerden kaynaklanırken, akışkan gerilmeleri basınç işi üretir.
Genel enerji denklemi tüm unsurları birleştirir: depolanan enerji, ısı, şaft işi ve normal gerilmeler nedeniyle basınç işi.
Bu denklem, ısı transferi, şaft çalışması ve kontrol yüzeyindeki basınç kuvvetlerini içeren akışkan sistemlerinde enerji tasarrufunu temsil eder.

kontrol hacminde enerjinin korunumu

Sabit akış koşulları altında çalışan bir türbini düşünün. Kontrol hacmi, bir noktadan giren ve diğerinden çıkan akışkanla türbinin etrafına çizilir. Türbin, mekanik iş (mil işi) gerçekleştiren akışkandan enerji çeker.

 Sabit akış sistemleri için, depolanan enerjinin zaman türevi, kontrol hacmi içinde enerji birikimi olmadığından sıfır olur. Bu, enerji denklemini şu şekilde basitleştirir:

<img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;">

 Türbin şaftı tarafından yapılan işe odaklandığımız ve ihmal edilebilir ısı transferi varsaydığımız için, Q̇ ≈ 0. Bu nedenle, enerji denklemi şu şekilde daha da basitleştirilir:

<img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;">

 Akış iki bileşene ayrılır: türbine giren akışkan (giriş) ve türbinden çıkan akışkan (çıkış). Her iki noktadaki kütlesel debi sabittir ve giriş ve çıkıştaki enerji akışı şu şekilde verilir:

<img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;">

 Burada:

-ṁ kütlesel debidir.

- ũ1, V_1 ve z_1 girişteki iç enerjiyi, hızı ve yüksekliği ifade eder,

- ũ2, V_2 ve z_2 çıkıştaki iç enerjiyi, hızı ve yüksekliği ifade eder,

 Tipik bir türbinde, akışkanın türbinin içinden geçtikçe iç ve kinetik enerjisi azalır, yararlı şaft işi yapılmasıyla sonuçlanır. Bir türbinin V_1=50 m/s giriş hızı, V_2= 20 m/s çıkış hızı, z_1=100 m giriş yüksekliği ve z_2=90 m çıkış yüksekliği ile çalıştığını varsayalım. İç enerji değişiminin kinetik ve potansiyel enerji değişimlerine kıyasla küçük olduğunu ve kütlesel debinin 10 kg/s olduğunu varsayalım.

<img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;">

 Sonuç olarak, türbin akan akışkandan enerji çekerek yaklaşık 11,48 kW mekanik güç üretir.

Kontrol Hacminde Enerjinin Korunumu

Termodinamiğin birinci yasası, bir sistemde depolanan toplam enerjinin değişim hızının, bir sisteme aktarılan net ısı ve iş oranına eşit olduğunu belirtir.

Education

JoVE Core

Civil Engineering

İnşaat Mühendisliği

Unit 1

Ünite 1

Finite Control Volume Analysis

Sonlu Kontrol Hacmi Analizi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

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

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...

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

Turbine Work from Energy Changes | 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

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

The first law of thermodynamics states that the rate of change of total stored energy in a system equals the net rate of heat and work transferred into a ...

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this ...

/files/media/science-education/science-education-thumbs/14702.jpg

conservation-of-energy-approach-to-system-analysis

Conservation of Energy Approach to System Analysis

Source: Ricardo Mejia-Alvarez and Hussam Hikmat Jabbar, Department of Mechanical Engineering, Michigan State University, East Lansing, MI
The purpose of ...

First Law of Thermodynamics

Energy Conservation

Energy can be converted from one form into another, but all of the energy present before a change occurs always exists in some form ...

What is Energy?

The universe is composed of matter in different forms, and all forms of matter contain energy. &#xA0;The different forms of energy on Earth originate from ...

Energy and Work

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

Enthalpy

Conservative Forces

According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the ...

Mechanism of heat transfer

Understanding heat transfer mechanisms is essential for understanding how our bodies maintain balance in different environmental conditions. When the ...

Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

Energy Transfer in Chemical Reactions

Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ...

Coupled Reactions

Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are ...

endergonic-and-exergonic-reactions-in-the-cell

Endergonic and Exergonic Reactions in the Cell

If energy releases during a chemical reaction, then the resulting value&#160;will be a negative number. In other words, reactions that release energy have ...

An Introduction to Free Energy

How can we compare the energy that releases from one reaction to that of another reaction? We use a measurement of free energy to quantitate these energy ...

gibbs-free-energy-and-thermodynamic-favorability

Gibbs Free Energy and Thermodynamic Favorability

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or ...

Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperatures are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).

Turbine Work from Energy Changes

Description

Transcript

Tags

More videos by Standards