Steam

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Module 16.1

Equations

SC-GCM-118 CM Issue 4

©

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Equations

Block 1: Introduction

Equation number Equation

There are no equations in Block 1

Block 2: Steam engineering principles and heat transfer

Thermodynamic temperature 2.1.1 Density of a material 2.1.2 Where: r = Density (kg/m³) m = Mass (kg) V = Volume (m³) vg = Specific volume (m³/kg)

Specific gravity of a material 2.1.3

Energy transfer equation 2.1.4 Where:

Q = Quantity of energy (kJ) m = Mass of the substance (kg)

cp = Specific heat capacity of the substance (kJ/kg °C )

DT= Temperature rise of the substance (°C)

Change in entropy 2.1.5

Change in specific entropy 2.1.6

(3)

Enthalpy of evaporation of wet steam 2.2.2 _Where:

hfg= Enthalpy of evaporation (Latent heat) (kJ/kg)

c = Dryness fraction

Total enthalpy of wet steam 2.2.3 Where:

hf = Liquid enthalpy (Sensible heat) (kJ/kg)

hfg= Enthalpy of evaporation (Latent heat) (kJ/kg)

Specific volume of wet steam 2.2.4 _Where:

vg = Specific volume of dry steam at same pressure

Flash steam produced from hot water and condensate

2.2.5 Where: P1 = Initial pressure P2 = Final pressure hf = Liquid enthalpy (kJ/kg) hfg= Enthalpy of evaporation (kJ/kg) Carnot efficiency 2.3.1 Where:

Ti = Temperature at turbine inlet (K)

Te = Temperature at turbine exhaust (K)

Rankine efficiency

2.3.2 _Where:

Hi= Heat at turbine inlet (kJ/kg)

He= Heat at turbine exhaust (kJ/kg)

(4)

Daltons law of partial pressures 2.4.1

Heat transfer by conduction through a layer (Fouriers law)

2.5.1 Where:

Q = Heat transferred per unit time (W)

k = Thermal conductivity of the material (W/m K or W/m°C) A = Heat transfer area (m²)

DT = Temperature difference across the material (K or °C) = Material thickness (m)

Heat transfer by convection (Newtons law of cooling) 2.5.2 Where:_{Q = Heat transferred per unit time (W)}

h = Convective heat transfer coefficient of the process (W/m² °C) A = Heat transfer area of the surface (m²)

DT = Temperature difference between the surface and the bulk fluid (K or °C)

General heat transfer

Where:

Q = Heat transferred per unit time (W)

2.5.3 U = Overall heat transfer coefficient (W/m² °C) A = Heat transfer area (m²)

DT = Temperature difference between the primary and secondary fluid (K or °C)

Note: Q will be a mean heat transfer rate (QM) if DT is a mean

temperature difference (DTLM or DTAM).

Arithmetic mean temperature difference (AMTD or DTAM)

2.5.4 _Where:

Ts = Steam temperature (°C)

T1 = Secondary fluid in temperature (°C)

(5)

Log mean temperature difference (LMTD or DTLM)

2.5.5

Where:

Ts = Steam temperature (°C)

T1 = Secondary fluid in temperature (°C)

T2 = Secondary fluid out temperature (°C)

ln = A mathematical function known as natural logarithm

Rate of heat transfer across a barrier knowing the thickness and conductivity

2.5.6 Where:

Q = Heat transferred per unit time (W ) A = Heat transfer area (m²)

DT = Temperature difference across the barrier (°C)

_/

k = Barrier thickness / material thermal conductivity

Rate of heat transfer across a barrier knowing thermal resistance

2.5.7 Where:

Q = Heat transferred per unit time (W ) A = Heat transfer area (m²)

DT = Temperature difference across the barrier (°C) R = Thermal resistance of the barrier (m2 _{°C / W)}

Resistivity from conductivity 2.5.8

Where:

r = Thermal resistivity (m°C / W) k = Thermal conductivity (W / m°C)

Thermal transmittance (heat transfer coefficient) from thermal resistance

2.5.9

Where:

U = Thermal transmittance of the barrier (W / m2 _°C)

(6)

Thermal transmittance (U) from the individual thermal resistances

2.5.10 Where:_R

1= Resistance of the air film

R2= Resistance of the condensate film

R3= Resistance of the scale film on the steam side

R4= Resistance of the of the metal wall

R5= Resistance of the scale film on the water side

R6= Resistance of the product film

Thermal transmittance (U) from the individual thicknesses and conductivities

2.5.11

Energy requirement for a non-flow application (e.g. batch or tank)

2.6.1 Where:

Q = Mean heat transfer rate (kW (kJ/s)) m = Mass of the fluid (kg)

cp = Specific heat capacity of the fluid (kJ/kg °C)

DT = Increase in fluid temperature (°C) t = Time for the heating process (seconds)

(7)

Heat transfer of condensing steam 2.6.3 Where:

Q = Mean heat transfer rate (kW or kJ/s) ms= Mean steam consumption (kg /s)

hfg= Specific enthalpy of evaporation of steam (kJ/kg)

Energy balance between steam and secondary fluid of a non-flow process

Where:

2.6.4 ms= Mean steam consumption rate (kg /s)

Q = Mean heat transfer rate (kW (kJ/s)) m = Mass of the secondary fluid (kg)

cp = Specific heat capacity of the secondary fluid (kJ/kg °C)

DT= Temperature rise of the secondary fluid (°C) t = Time for the heating process (seconds)

Energy requirement for a flow-type application (e.g heat exchanger) 2.6.5 Where:

Q = Mean heat transfer rate (kW)

m = Mean secondary fluid flowrate (kg /s)

cp = Specific heat capacity of the secondary fluid (kJ/kg K) or (kJ/kg °C)

DT= Temperature rise of the secondary fluid (K or °C)

Energy balance between steam and fluid of a flow-type application

Where:

Q = Mean heat transfer rate (kW (kJ/s))

m = Mass flowrate of the secondary fluid (kg /s)

DT= Temperature rise of the secondary fluid (°C)

Mean steam consumption of a flow type application

Where:

m = Mass flowrate of the secondary fluid (kg /s)

(8)

Mean steam consumption of a flow type application

2.6.8 _Where:

ms= Mean steam consumption rate (kg /s)

To determine the required steam flowrate from a kW rating 2.8.1

To determine the steam flowrate for a steam injection process

2.11.1 Where:ms= Mean steam flowrate (kg /s)

hg = Specific total enthalpy of the steam upstream

of the control valve (kJ/kg) T = Final temperature of the water

cp = Specific heat capacity of the water (kJ/kg °C)

Steam consumption to provide tank heat losses 2.11.2

Where:

ms= Mean steam flowrate to provide the heat losses from the tank (kg /s)

Q = Q(sides) + Q(surface) (kW)

2256.7 = Enthalpy of evaporation at atmospheric pressure (kJ/kg)

Mass and heat balance for steam injection into a tank

Where:

2.11.3 m = Initial mass of water in the tank (kg) ms= The mass of steam to be injected (kg)

h1 = The heat in the water at the initial temperature (kJ/kg)

h2 = The heat in the water at the final temperature (kJ/kg)

(9)

Steam consumption by injection into a tank

2.11.4 Where:

ms= The mass of steam to be injected (kg)

m = Initial mass of water in the tank (kg)

h1 = The heat in the water at the initial temperature (kJ/kg)

h2 = The heat in the water at the final temperature (kJ/kg)

hg = The total enthalpy of the steam upstream of the control valve (kJ/kg)

Steam start-up load to bring steam pipework to operating temperature

2.12.1 Where:_m_s _{= Mean rate of condensation of steam (kg/h)}

W = Total weight of pipe plus flanges and fittings (kg) Ts = Steam temperature (°C)

Tamb = Ambient temperature (°C)

cp = Specific heat of pipe material (kJ/ kg °C)

hfg = Enthalpy of evaporation at operating pressure (kJ/ kg)

t = Time for warming up (minutes)

Steam running load to keep a steam main at operating temperature

2.12.2 Where:ms= Rate of condensation (kg /h)

Q = Heat emission rate (W/m)

L = Effective length of pipe allowing for flanges and fittings (m) f = Insulation factor (dimensionless)

hfg= Enthalpy of evaporation at operating pressure (kJ/ kg)

Note: The constant 3.6 gives the answer in kg/ h Steam condensing rate for air heating equipment

2.12.3

Where:

ms= Rate of steam condensation (kg /h)

V = Volumetric flowrate of air being heated (m³/s) DT= Air temperature rise (°C)

cp = Specific heat of air at constant pressure (kJ/ m³ °C)

hfg= Enthalpy of evaporation of steam in the coils (kJ/ kg)

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Steam condensing rate for horizontal pipes in still air

2.12.4 Where:ms = Rate of steam condensation (kg/h)

Q = Heat emission from pipe (W/m) L = Effective length of pipes (m)

hfg = Enthalpy of evaporation at the working pressure (kJ/ kg)

Note: The constant 3.6 gives the answer in kg/h Mean steam flowrate to a storage calorifier

2.13.1 Where:ms = Mean rate of condensation (kg/ h)

m = Mass of water heated (kg) cp = Specific heat of water (kJ/ kg °C)

DT = Change in temperature of water (°C) hfg = Enthalpy of evaporation of steam (kJ/kg)

t = Recovery time to heat the water (hours)

Steam consumption of drying cylinders

2.14.1 Where:ms = Mass flowrate of steam (kg /h)

Ww= Throughput of wet material (kg/h)

Wd = Throughput of dry material (kg/h)

T2 = Temperature of material leaving the machine (°C)

T1 = Temperature of material entering the machine (°C)

hfg = Enthalpy of evaporation of steam in cylinders (kJ/kg)

The kinetic energy in steam

2.16.1 Where:E = Kinetic energy (kJ) m = Mass of the fluid (kg) u = Velocity of the fluid (m/s)

g = Acceleration due to gravity (9.806 65 m/s²)

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Velocity of steam passing through an orifice in terms of kinetic energy

2.16.2 Where:

u = Velocity of the fluid (m /s) E = Kinetic energy (kJ)

g = Acceleration due to gravity (9.806 65 m /s²)

J= Joules mechanical equivalent of heat (101.972 m kg/kJ) m = Mass of the fluid (kg)

Velocity of steam passing through an orifice in terms of heat drop 2.16.3 _Where:

u = Veolocity of the fluid (m/s) h = Heat drop per unit mass (kJ/kg)

Mass flow of steam through an orifice 2.16.4

Velocity of steam passing through an orifice in terms of heat drop

2.16.5

Where:

u = Velocity of the fluid in m/s h = Heat drop in J/kg

2 = Constant of proportionality incorporating the gravitational constant g.

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Block 3: The boiler house

Stress in a boiler shell resulting from boiler pressure

3.2.1 Where:

s = Hoop stress (N /m²)

P = Boiler pressure (N /m² = bar x 105₎

D = Diameter of cylinder (m) = Plate thickness (m)

Relating boiler pressure to heat transfer rate 3.2.2

Where:

P = Boiler pressure (N /m² = bar x 105₎

Q = Heat transfer rate (kW)

To determine the evaporation factor of a boiler from its From & At rating

3.5.1

Where:

A = Specific enthalpy of evaporation at atmospheric pressure. B = Specific enthalpy of steam at operating pressure.

C = Specific enthalpy of water at feedwater temperature.

To determine the actual evaporation rate of a boiler from its kW rating and the energy required to be added to the feedwater to make steam

3.5.2

Where:

m = Steam output (kg/h) Q = Boiler rating (kW)

To determine boiler horse power from heat transfer area 3.5.3

Where:

BoHP = Boiler horsepower

Calculating boiler efficiency 3.6.1

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To determine the TDS of a sample by the density method 3.12.1

To determine the TDS of a sample by the conductivity method 3.12.2

To correct the conductivity of a sample at a temperature from 25°C 3.12.3 Where:

sT = Conductivity at temperature T (µS / cm)

s25= Conductivity at 25°C (µS / cm)

a = Temperature coefficient, per °C (Typically 0.02 / °C or 2%°C) T = Temperature (°C)

The electrical resistance of a conductivity probe

3.12.4 _Where:

R = Resistance (Ohm) K = Cell constant (cm-1₎

s = Conductivity (S / cm)

To determine the blowdown rate of a boiler

3.12.5 _Where:

F = Feedwater TDS (ppm). S = Steam generation rate (kg / h). B = Required boiler water TDS (ppm).

Ohms Law 3.16.1 _Where: I = Current (amperes) V = Voltage (volts) R = Resistance (ohms) Capacitance Law 3.16.2 Where: C = Capacitance (farad)

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Steam injection required to power a steam deaerator

3.21.1 Where:

ms= Mass of steam to be injected (kg / h)

m = Maximum boiler output at the initial feedwater temperature (kg / h) h1 = Enthalpy of water at the initial temperature (kJ / kg)

h2 = Enthalpy of water at the required temperature (kJ / kg)

hg = Enthalpy of steam supplying the control valve (kJ / kg)

Sizing a control valve for saturated steam

Where:

3.21.2 ms= Steam mass flowrate (kg /h)

Kv = Valve coefficient required

P1 = Pressure upstream of the control valve (bar a)

P2 = Pressure downstream of the control valve (bar a)

Sizing a control valve for liquid

3.21.3 Where:

V = Volumetric flowrate (m3_/h)

Kv = Valve coefficient required

DP= Pressure drop across the valve (bar) G = Relative density of fluid (water = 1)

Steam storage capacity of an accumulator 3.22.1

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To determine the Absolute or Dynamic viscosity of a fluid by dropping a sphere through a fluid

Where:

4.1.1 µ = Absolute (or dynamic) viscosity (Pa s)

D r = Difference in density between the sphere and the liquid (kg / m3₎

g = Acceleration due to gravity (9.81 m/ s2₎

r = Radius of sphere (m) u =

To determine the Kinematic viscosity of a fluid

4.1.2 _Where:

v = Kinematic viscosity (centistokes) µ = Dynamic viscosity (Pa s)

r = Density (kg/m3₎

To determine the Reynolds number of a fluid in a circular pipe

4.1.3 Where:_R

e= Reynolds number (dimensionless)

r = Density (kg /m3₎

u = Mean velocity in the pipe (m/s) D = Internal pipe diameter (m) µ = Dynamic viscosity (Pa s)

To determine volumetric flowrate from velocity 4.1.4 Where:

qv = Volume flow (m3/s)

A = Cross sectional area of the pipe (m2₎

u = Velocity (m/ s)

To determine mass flowrate from volumetric flowrate

4.1.5 _Where:

qm= Mass flow (kg/s)

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To determine mass flowrate from velocity

4.1.6 Where:

qm = Mass flow (kg/ s)

A = Cross sectional area of the pipe (m2₎

u = Velocity (m /s)

vg = Specific volume (m3/ kg)

To determine the turndown ratio of a steam flowmeter 4.2.1

Bernoullis Equation for a liquid

4.2.2 Where:_P

1 and P2 = Pressure at points within a system (Pa)

u1 and u2 = Velocities at corresponding points within a system (m/s)

h1 and h2 = Relative vertical heights within a system (m)

r = Density (kg/ m3₎

g = Gravitational constant (9.81 m/s²)

Bernoullis Equation multiplied throughout by rg

4.2.3 Where:

P1 and P2 = Pressure at points within a system (Pa)

h1 and h2 = Relative vertical heights within a system (m)

g = Gravitational constant (9.81 m/s²)

Bernoullis Equation with constant potential energy terms 4.2.4

Where:

P1 and P2 = Pressure at points within a system (Pa)

Bernoullis Equation with constant potential energy terms and frictional losses

4.2.5 _Where:

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The pressure drop for a liquid equals the friction loss 4.2.6 Where:

P1 = Upstream pressure (Pa)

P2 = Downstream pressure (Pa)

hf = Friction loss (Pa)

Potential energy 4.2.7 Where:

m = Mass of all the molecules directly between and including molecule 1 and molecule 2.

g = Gravitational constant (9.81 m/s2₎

h = Cumulative height of molecules above the hole

Kinetic energy 4.2.8

Where:

m = Mass of the object (kg)

u = Velocity of the object at any point (m/s)

Potential energy at = Kinetic energy at the start of process the end of process 4.2.9

Where:

m = Mass of the object (kg)

h = Height of the object above a reference point (m)

Velocity of liquid through an orifice 4.2.10

Where:

u = Velocity (m/ s)

h = Pressure head (m)

Volumetric flowrate of liquid through an orifice

Where:

4.2.11 qv = Volumetric flowrate (m3/s)

C = Coefficient of discharge (dimensionless) A = Area of orifice (m2₎

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Volumetric flowrate of liquid is proportional to the square root of pressure drop

4.2.12

Where:

qv = Volumetric flowrate (m3/ s)

Dp= Pressure drop (m)

The liquid velocity measured by a Pitot tube 4.2.13

Where:

u1 = The fluid velocity in the pipe

DP= Static pressure - dynamic pressure r = The fluid density

To determine the b ratio for an orifice plate 4.3.1

Note: Diameters must be in the same unit of measurement

To determine the vortex shedding frequency around a bluff body

4.3.2 Where:

f = Shedding frequency (Hz)

Sr = Strouhal number (dimensionless) u = Mean pipe flow velocity (m/s) d = Bluff body diameter (m)

The volumetric flowrate from the shedding frequency

4.3.3 Where:

qv = Volumetric flowrate (m3/s)

A = Cross sectional area of the orifice (m2₎

f = Shedding frequency (Hz)

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Percentage error when using a velocity sensing meter which is not pressure compensated

4.4.1

Where:

e = Flow error expressed as a percentage of the actual flow Specified r = Density of steam at the specified steam line pressure Actual r = Density of steam at the actual line pressure

Percentage error when using a pressure difference meter which is not pressure compensate

4.4.2

Where:

e = Percentage flow error

Actual r = Density of steam at actual pressure (kg/m3₎

Specified r = Density of steam at specified pressure (kg /m3₎

To determine the density of steam with known dryness fraction

4.4.3 _Where:

r = Density of steam with dryness fraction c ng= Specific volume of dry steam

Approximation of relationship between indicated and actual flowrate with a deviation in dryness fraction

4.4.4

Actual value of superheated steam flowing through a flowmeter calibrated for saturated steam

4.4.5

Block 5: Basic control theory

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(A x DP) + Friction allowance = F

Block 6: Control hardware: Electric/pneumatic actuation

Closing force to close a valve 6.1.1 Where:

A = Valve seating area (m2₎

DP = Differential pressure (kPa) F = Closing force required (kN)

Calculate valve Kv for liquids

6.3.1 Where:

Kv = Flow of liquid that will create a pressure drop of 1 bar (m³/ h bar)

V = Flowrate (m³/h)

G = Relative density /specific gravity of the liquid (dimensionless). DP = Pressure drop across the valve (bar)

Volumetric flow of water through a valve 6.3.2 Where:

V = Flowrate (m³/h)

Kv = Flow of liquid to create a pressure drop of 1 bar (m³/h bar)

DP = Pressure drop across a valve (bar)

The flow of liquid through a constant bore pipe relative to pressure loss

6.3.3

Where:

V1= Flowrate at pressure loss P1

V2= Flowrate at pressure loss P2

Valve authority

6.3.4 Where:

N = Valve authority

DP1 = Pressure drop across a fully open control valve

DP2 = Pressure drop across the remainder of the circuit

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Critical pressure ratio for dry steam and gases 6.4.1

Where:

g = Isentropic exponent of the steam or gas

Speed of sound in steam

Where:

6.4.2 C = Speed of sound in steam (m / s) 31.6 = Constant of proportionality

g = Steam isentropic exponent (1.135 : saturated, 1.3 : superheated) R = 0.461 5 the gas constant for steam (kJ / kg)

T = Absolute steam temperature (K)

Steam flow through a valve under critical flow conditions 6.4.3 Where:

ms= Mass flow through a valve (kg/h)

Kv= Valve capacity (m3/h bar)

P1 = Upstream pressure (bar a)

Volumetric flow through an equal pecentage valve

Where:

6.5.1 Vx = Volumetric flow through the valve at lift H.= (ln t) H Note: In is a mathematical function known as natural logarithm.

t = Valve rangeability (ratio of the maximum to minimum

controllable flowrate, typically 50 for a globe type control valve) H = Valve lift (0 = closed, 1 = fully open)

Vmax = Maximum volumetric flow through the valve

Required capacity of a water control valve

6.5.2 _Where:

Kvr = The actual valve capacity required by the installation (m³/h bar)

V = Flowrate through the valve (m3_/h)

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Percentage lift of an equal percentage valve in terms of relative flow

6.5.3

Where:

H% = Percentage lift In = Natural logarithm

V = Flow through the valve at lift H (m3_/h)

t = Valve rangeability

Vmax = Maximum flow through the valve at full lift (m3/h)

Percentage lift of an equal percentage valve in terms of relative Kv

6.5.4 Where:

H% = Percentage lift In = Natural logarithm

Kvr = Required capacity at lift H (m3/h bar)

t = Valve rangeability

Kvs = Valve capacity full open (m3/h bar)

The required capacity for a steam valve under sub-sonic flow

6.5.5 Where:

Kvr= Required capacity at lift H (m3/h bar)

ms = Steam mass flowrate (kg/h)

P2 = Downstream pressure (bar a)

x = (P1 - P2)/ P1

Block 7: Control hardware: Self-acting actuation

Stem force required to close a control valve

7.1.1 _Where:

d = Diameter of valve orifice (mm) DP = Differential pressure (bar)

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There are no equations in Block 8

Block 9: Safety valves

Flow area of a safety valve 9.1.1

Where:

d = The area of the inlet port at its narrowest point

Curtain area of a safety valve 9.1.2 Where:

d1 = Minimum area of opening between the valve and seat

L = Maximum lift from seat to valve

Required opening force for a safety valve with the spring housing vented via the discharge vent pipe

9.2.1 Where:

PV = Fluid inlet pressure

AN = Nozzle area

FS = Spring force

PB = Backpressure

Required opening force for a safety valve with the spring housing vented to atmosphere

9.2.2 Where:

AN = Nozzle area

FS = Spring force

PB = Backpressure

AD = Disc area

Required opening force for a safety valve with the spring housing vented via the discharge vent pipe and taking into effect the build-up backpressure

9.2.3 Where:

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Required opening force for a balanced safety valve 9.2.4 Where:

AN = Nozzle area

FS = Spring force

Cold differential pressure 9.3.1 Where:

CDSP = Cold differential set pressure RISP = Required installed set pressure CBP = Constant backpressure

Coefficient of discharge 9.4.1

Where:

Kd= Coefficient of discharge

Critical pressure ratio

9.4.2 Where:

PB = Critical backpressure (bar a)

P1 = Actual relieving pressure (bar a)

k = Isentropic coefficient of the gas or vapour at the relieving conditions

AD-Merkblatt valves - Minimum flow area for steam

9.4.3 Where:

AO = Minimum cross sectional flow area (mm2)

c = Pressure medium coefficient m = Mass flow to be discharged (kg / h) aW = Outflow coefficient

PR = Absolute relieving pressure (bar a)

AD-Merkblatt valves - Minimum flow area for dry gases and air

Where:

AO = Minimum cross sectional flow area (mm2)

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AD-Merkblatt valves - Minimum flow area for liquids

Where:

9.4.5 AO = Minimum cross sectional flow area (mm2)

m = Mass flow to be discharged (kg / h) aW = Outflow coefficient

r = Density (kg / m3₎

DP = PR - PB

PB = Absolute backpressure (bar a)

Compressibility factor for compressible steam and dry gases

Where:

9.4.6 Z = Compressibility factor

PR = Safety valve relieving pressure (bar a)

n = Specific volume of the gas at the actual relieving pressure and temperature (m3_{/ kg)}

M = Molar mass (kg / kmol)

Ru= Universal gas constant (8 314 Nm / kmol K)

T = Actual relieving temperature (K)

Proportion of vapour in two phase discharge

9.4.7 Where:

n = The proportion of discharge fluid which is vapour hf1 = Enthalpy of liquid before the valve (kJ / kg)

hf2 = Enthalpy of liquid after the valve (kJ / kg)

hfg2= Enthalpy of evaporation after the valve (kJ / kg)

ASME (API RP 520) valves - Minimum flow area for steam

9.4.8 Where:

AO = Required effective discharge area (in2)

m = Required mass flow through the valve (lb / h) PR = Upstream relieving pressure (psi a)

Kd = Effective coefficient of discharge

KSH= Superheat correction factor

ASME (API RP 520) valves - Minimum flow area for dry gases and air

Where:

V = Required volume flow through the valve (ft3_{/ min)}

9.4.9 T = Relieving temperature (°R) Z = Compressibility factor

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ASME (API RP 520) valves - Minimum flow area for liquids

Where:

9.4.10 V1 _{= Required volume flow through the valve (U.S. gal / min)}

Kd = Effective coefficient of discharge (specified by the manufacturer)

Kµ = Viscosity factor

KW= Backpressure correction factor for liquids (bellows balanced valves only)

G = Specific gravity (ratio of molar mass of the fluid to the molar mass of air

PR = Upstream relieving pressure (psi a)

PB = Absolute backpressure (psi a)

ASME (API RP 520) valves - Nozzle gas constant

9.4.11

Where:

Cg = Nozzle gas constant

k = Isentropic coefficient of the gas or vapour at the relieving conditions

ASME (API RP 520) valves - Backpressure correction factor

9.4.12 Where:

KB= Backpressure correction factor

C1= Capacity of valve with backpressure applied

C2= Capacity of valve when discharging to atmosphere

ASME (API RP 520) valves - Bellows balanced valves 9.4.13

Where:

PB = Backpressure (psi g)

PS = Set pressure (psi g)

ASME (API RP 520) valves - Conventional valves 9.4.14

Where:

PB = Backpressure (psi g)

PR = Relieving pressure (psi g)

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ASME (API RP 520) valves - Reynolds number: Imperial units

9.4.16 Where:

Re = Reynolds number

V = Volume flow to be discharged (U.S. gal / min) m = Mass flow to be discharged (kg / h)

µ = Dynamic viscosity (Imperial cP, Metric Pa s) AO= Discharge area (Imperial in2, Metric mm2)

BS 6759 valves - Minimum orifice area for steam

Where:

9.4.17 AO = Flow area (mm2)

m = Mass flow to be discharged (kg / h) PR = Absolute relieving pressure (bar a)

Kdr = Derated coefficient of discharge

KSH= Superheat correction factor

BS 6759 valves - Minimum orifice area for air

9.4.18 Where:_A

O = Flow area (mm2)

V = Volumetric flow to be discharged (l / s) PR = Absolute relieving pressure (bar a)

T = Inlet temperature (K)

BS 6759 valves - Minimum orifice area for dry gases

Where:

AO = Flow area (mm2)

9.4.19 m = Mass flow to be discharged (kg / h) PR = Absolute relieving pressure (bar a)

Cg = Nozzle gas constant

Z = Compressibility factor T = Inlet temperature (K)

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BS 6759 valves - Minimum orifice area for liquids

Where:

9.4.20 A_{m = Mass flow to be discharged (kg / h)}O = Flow area (mm2)

Kdr= Derated coefficient of discharge

Kµ = Viscosity correction factor

r = Density (kg / m3₎

DP = PR - PB

PB = Absolute backpressure (bar a)

BS 6759 valves - Minimum orifice area for hot water

9.4.21 Where:_A

O = Flow area (mm2)

Q = Hot water heating capacity (kW) PR = Absolute relieving pressure (bar a)

Kdr= Derated coefficient of discharge

BS 6759 valves - Nozzle gas constant 9.4.22

Where:

k = Isentropic coefficient of gas or vapour

EN ISO 4126 valves - Minimum orifice area for steam, air and dry gas at critical flow

9.4.23 Where:

A = Flow area (not curtain area) (mm2₎

m = Mass flowrate (kg / h)

C = Function of the isentropic exponent Kdr= Certified derated coefficient of discharge

Po = Relieving pressure (bar a)

ng = Specific volume at relieving pressure and temperature (m³/kg)

EN ISO 4126 valves - Minimum orifice area for wet steam at critical flow

9.4.24 Where:_{A = Flow area (not curtain area) (mm}2₎

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EN ISO 4126 valves - Minimum orifice area for air and dry gas at sub-critical flow

9.4.25 Where:

A = Flow area (not curtain area) (mm2₎

C = Function of the isentropic exponent Kdr = Certified derated coefficient of discharge

Kb = Theoretical correction factor for sub-critical flow

EN ISO 4126 valves - Minimum orifice area for liquids

Where:

9.4.26 A = Flow area (not curtain area) (mm2₎

Kdr = Certified derated coefficient of discharge

Kv = Viscosity correction factor

Pb = Backpressure (bar a)

Safety valve vent pipe diameter

9.5.1 Where:

d = Pipe diameter (mm)

Le = Equivalent length of pipe (m)

m = Discharge capacity (kg / h)

P = Safety valve set pressure (bar g) x 0.1

vg = Specific volume of steam at the pressure (P) (m3 / kg)

Reaction force at the end of a safety valve vent pipe

Where:

9.5.2 F = Reaction force at the point of discharge to atmosphere (newtons) m = Discharge mass flowrate (kg / s)

(30)

Sound power level at the safety valve outlet

Where:

LP = Sound power level in dB (A)

9.5.3 m = Mass flow (kg / h)

u = Speed of sound in an ideal gas (m / s), k = Isentropic coefficient of the gas

Ru= Universal gas constant (8 314 J / kmol K)

T = Absolute gas temperature at the safety valve outlet (K) M = Molar mass (kg / kmol)

Sound pressure level at the safety valve outlet 9.5.4 Where:

L = Sound pressure level in dB (A) LP = Sound power level in dB (A)

R = Distance from the source (m)

Sound power level from EN ISO 4126 9.5.5 Where:_L_P _{= Sound power level in dB (A)}

DA= Discharge pipe bore (mm)

= Specific volume at relieving pressure and temperature (m3_{/ kg)}

u = Velocity of fluid in the outlet pipe (m / s)

Block 10: Steam distribution

The SI based DArcy equation for determining pressure drop due to frictional resistance

10.2.1 Where:_h_f _{= Head loss to friction (m)}

f = Friction factor (dimensionless) L = Length (m)

u = Flow velocity (m/s)

g = Gravitational constant (9.81 m /s²) D = Pipe diameter (m)

(31)

The Imperial based DArcy equation for determining pressure drop due to frictional resistance

Where:

10.2.2

hf = Head loss to friction (m)

f = Friction factor (dimensionless) L = Length (m)

u = Flow velocity (m /s)

g = Gravitational constant (9.81 m/s²) D = Pipe diameter (m)

Friction factor for turbulent fluids (Colebrook-White formula)

10.2.3 Where:

f = Friction factor (Relates to the SI Moody chart) kS = Absolute pipe roughness (m)

D = Pipe bore (m)

Re = Reynolds number (dimensionless)

SI based friction factors - f 10.2.4

Where:

f = Friction factor Re = Reynolds number

Imperial based friction factors - f 10.2.5 Where: f = Friction factor Re = Reynolds number Reynolds number Where: Re = Reynolds number 10.2.6 r = Density of water (kg /m3₎ u = Velocity of water (m/s) D = Pipe diameter (m)

m = Dynamic viscosity of water (kg /m s)

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Pressure factor

10.2.8 _Where:

F = Pressure factor

P1 = Factor based on the inlet pressure

P2 = Factor based on the pressure at a distance of L metres of pipe

L = Equivalent length of pipe (m)

Pressure drop formula 1

10.2.9 Where:

P2 = Downstream pressure (bar a)

L = Length of pipe (m) m = Mass flowrate (kg /h) D = Pipe diameter (mm)

Pressure drop formula 2 (Maximum pipe length: 200 metres)

10.2.10 Where:

DP = Pressure drop (bar) L = Length of pipe (m)

vg = Specific volume of steam (m³/kg)

m = Mass flowrate (kg /h) D = Pipe diameter (mm)

Thermal expansion of pipe

10.4.1 Where:_{L = Length of pipe between anchors (m)}

DT = Temperature difference between ambient temperature and operating temperatures (°C)

a = Expansion coefficient (mm/m °C x 10-3₎

Block 11: Steam trapping

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Pressure drop across a valve in a liquid system

12.2.1 Where:

DP = Pressure drop across the valve (bar)

G = Specific gravity of the liquid (non-dimensional) V = Flowrate of liquid (m³/ h)

Kv = Valve flow coefficient (m³/h bar)

Equivalent water flowrate through a check valve

12.3.1 Where:

Vw = Equivalent water volume flowrate (m³/ h) r = Density of the liquid (kg/m³)

V = Volume flowrate of liquid (m³ /h)

Converting water mass flow to volumetric flow 12.3.2 Where:

V = Volume flowrate (m³/h) m = Mass flowrate (kg /h) ng = Specific volume (m³/ kg)

Largest particle size through a strainer screen 12.4.1 Where:

a = Mesh hole length b = Mesh hole width c = Particle size

Pressure drop across a steam valve

12.4.2 Where:

DP = Pressure drop across the valve (bar) ms = Steam flowrate (kg / h)

Kv = Valve flow coefficient (m3 / h bar)

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Block 13: Condensate removal

Calculating the heating area of a heat exchanger

13.2.1 Where:

A = Area of heating surface (m²) Q = Mean heat transfer rate (W)

U = Heat transfer coefficient (W/ m² °C) DTM = Mean temperature difference.

The heat exchanger temperature design constant

13.2.2 Where:

TDC = Temperature design constant of the heat exchanger Ts = Steam temperature (°C)

T1 = Secondary fluid inlet temperature (°C)

T2 = Secondary fluid outlet temperature (°C)

The steam temperature at any load

13.2.3 Where:

The secondary fluid inlet temperature at any load 13.2.4 Where:

The secondary fluid outlet temperature at any load

13.2.5 Where:

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Mean differential temperature between the primary and secondary fluids

13.3.1 Where:

DTM = Mean temperature difference.

Note: DTM may be either DTLM (LMTD) or DTAM (AMTD)

Q = Mean heat transfer rate (W)

U = Heat transfer coefficient (W /m² °C) A = Heating area (m²)

The secondary inlet temperature at any load

13.4.1 Where:_T_x _{= The secondary inlet temperature at any load factor x (°C)}

T1 = The secondary inlet temperature at full-load (°C)

T2 = The secondary outlet temperature at full-load (°C)

x = The load factor

The stall load for a constant flow secondary

13.5.1 Where:

A = The steam temperature in the steam space at full-load (°C) B = The secondary fluid outlet temperature (°C)

D = The backpressure equivalent saturated steam temperature (°C)

Calculating the stall load with a variable flow secondary

13.6.1 Where:

A = Steam temperature at full-load (°C)

B = Secondary fluid outlet temperature at full-load (°C) C = Secondary fluid inlet temperature at full-load (°C) D = Equivalent backpressure steam temperature (°C)

(36)

Block 14: Condensate recovery

Cost of fuel saved by returning condensate

Where:

X = Expected improvement in condensate return expressed as a

14.1.1 percentage between 1 and 100 A = Cost of fuel to provide 1 GJ of energy

B = Energy required per kilogram of make-up water to reach condensate temperature (kJ/kg).

C = Average boiler evaporation rate (kg/ h) D = Operational hours per year (h /year) E = Boiler efficiency (%)

Cost of water saved by returning condensate 14.1.2

Cost of effluent saved by returning condensate 14.1.3

Calculating pump delivery head

Where:

14.4.1 _h

d= Total delivery head

hs = Pressure required to raise the water to the desired level (static head)

hf = Pressure required to move the water through the pipes (friction head)

hp= Pressure in the condensate system

Calculate condensate velocity in a pipe 14.4.2

Block 15: Desuperheating

Calculate cooling water flowrate for a desuperheater