# Thermodynamics Steady Flow Energy Equation

### Thermodynamics - Steady Flow Energy Equation

Introduction

The steady flow energy equation relates to open systems working under steady conditions i.e in which conditions do not change with time.

The boundary encloses a system through which fluid flows at a constant rate, whilst heat transfer occurs and external work is done all under steady conditions ,that is , the rates of mass flow and energy flow are constant with respect to time.

The equation for steady flow ( the steady flow energy equation ) is generally written per unit mass as

q = heat transfer across boundary per unit mass
w = external work done by system per unit mass
z = fluid height
v = fluid velocity
h = fluid enthalpy ( u (internal energy + pv (pressure.specific volume)

Note in the examples below the system control volumes are defined by the red dashed line.

Heater.. The steady flow equation as applied to a fluid heater..

Potential energy (z) assumed to be constant..
Kinetic energy changes (1 to 2) assumed to be very small

Heater

w = 0 therefore
q = h2-h1

Turbine ..(Assumed Adiabetic Expansion)..The steady flow equation as applied to a turbine..

Potential energy (z) assumed to be constant..
Kinetic energy changes (1 to 2) assumed to be very small

Turbine

q = 0 therefore
w = h2-h1

Throttling ..(Assumed Adiabetic )...The steady flow equation as applied to a orifice..

Potential energy (z) assumed to be constant..
The higher velocity at orifice section is dissipated in tube downstream of the orifice and therefore the kinetic energies at 1 and 2 are similar

Orifice

q = w = 0 therefore
therefore h1 = h2

Potential energy (z) assumed to be constant..
Kinetic energy changes are assumed to be significant

Nozzle

q = w = 0 therefore
(v22 - v12 ) /2 = (h1 - h2 )