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

La prima legge della termodinamica afferma che il tasso di variazione dell'energia totale immagazzinata in un sistema è uguale al tasso netto di calore e lavoro trasferito in un sistema.
Per un volume di controllo che coincide con il sistema in un dato momento, il calore netto e il lavoro che entrano nel sistema sono uguali al calore netto e il lavoro che entrano nel volume di controllo.
Per questo sistema e per il volume di controllo coincidente, viene applicato il teorema di trasporto di Reynolds.
Il tasso totale di variazione dell'energia all'interno del volume di controllo è determinato sia dal tasso di variazione temporale dell'energia immagazzinata che dal flusso di energia netta attraverso il limite.
L'energia che scorre attraverso il confine include i contributi del calore e del lavoro, come il lavoro del pozzo e il lavoro a pressione.
Il lavoro dell'albero è il risultato di componenti rotanti come le turbine, mentre le sollecitazioni del fluido producono un lavoro di pressione.
L'equazione generale dell'energia combina tutti gli elementi: energia immagazzinata, calore, lavoro dell'albero e lavoro di pressione dovuto a sollecitazioni normali.
Questa equazione rappresenta la conservazione dell'energia nei sistemi a fluidi, incorporando il trasferimento di calore, il lavoro dell'albero e le forze di pressione sulla superficie di controllo.

conservazione dell'energia nel volume di controllo

Consideriamo una turbina che funziona in condizioni di flusso costante. Il volume di controllo è disegnato attorno alla turbina, con il fluido che entra in un punto e ne esce in un altro. La turbina estrae energia dal fluido, che esegue lavoro meccanico (lavoro dell'albero).

Per i sistemi a flusso stazionario, la derivata temporale dell'energia immagazzinata diventa zero, poiché non vi è accumulo di energia all'interno del volume di controllo. Ciò, semplifica l'equazione dell'energia in:

<img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;">

Poiché ci concentriamo sul lavoro svolto dall'albero della turbina e assumiamo un trasferimento di calore trascurabile, Q̇ ≈ 0. Pertanto, l'equazione dell'energia si semplifica ulteriormente in:

<img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;">

Il flusso è diviso in due componenti: il fluido che entra nella turbina (ingresso) e uno che esce dalla turbina (uscita). La portata di massa in entrambi i punti è costante e il flusso di energia all'ingresso e all'uscita è dato da:

<img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;">

Dove:

- ṁ è la portata di massa,

- ũ1 , V_1 e z_1 si riferiscono all'energia interna, alla velocità e all'altezza all'ingresso,

- ũ2 , V_2 e z_2 si riferiscono all'energia interna, alla velocità e all'altezza all'uscita,

In una tipica turbina, l'energia interna e cinetica del fluido, diminuisce mentre passa attraverso la turbina, il che si traduce in un utile lavoro all'albero. Supponiamo che una turbina funzioni con una velocità di ingresso di V_1=50 m/s, una velocità di uscita di V_2= 20 m/s, un'altezza di ingresso z_1=100 m e un'altezza di uscita z_2=90m. Supponiamo che la variazione di energia interna sia piccola rispetto alle variazioni di energia cinetica e potenziale e che la portata di massa is 10 kg/s.

<img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;">

Di conseguenza, la turbina produce circa 11,48 kW di potenza meccanica, estraendo energia dal fluido che scorre attraverso.

Conservazione dell'Energia nel Volume di Controllo

La prima legge della termodinamica afferma che il tasso di variazione dell'energia totale immagazzinata in un sistema è uguale al tasso netto di calore e lavoro trasferito in un ...

Education

Didattica

JoVE Core

Civil Engineering

Ingegneria Civile

Unit 1

Unità 1

Finite Control Volume Analysis

Analisi a volume di controllo finito

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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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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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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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.

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Turbine Work from Energy Changes

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