# Hot Water Heating Systems - a Design Procedure

## A hot water heating system design procedure - heat loss, boiler rating, heater units and more

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The design of a hot water heating system may follow a procedure as shown below:

- Calculate the heat loss from the rooms
- Calculate the boiler output
- Select heater units
- Select type, size and duty of circulation pump
- Make pipe scheme and calculate pipe sizes
- Calculate expansion tank
- Calculate safety-valves

### 1. Calculating Heat loss

Calculate transmission heat losses through walls, windows, doors, ceilings, floors etc. In addition heat loss caused by ventilation and infiltration of outdoor air must be calculated.

### 2. Boiler Rating

The rating of a boiler can be determined by

B = H (1 + x)(1)

where

B= boiler rating (kW)

H= total heat loss (kW)

x= margin for heating up - it is common to use values in the range 0.1 to 0.2

The correct boiler must be selected from manufacturer catalogs.

### 3. Selecting Room heaters

The rating of radiators and room heaters may be calculated by

R = H (1 + x)(2)

where

R= rating of heaters in room (W)

H= heat loss from the room (W)

x= margin for heating up the room - common values in the range 0.1 to 0.2

Heaters with correct ratings must be selected according the manufactures catalogues.

### 4. Sizing Pumps

The capacity of the circulation pump can be calculated as

Q = H / (h_{1}- h_{2}) ρ(3)

where

Q= volume of water (m^{3}/s)

H= total heat loss of plant (kW)

h_{1}= enthalpy flow water (kJ/kg) (4.204 kJ/kg.^{o}Cat 5^{o}C,4.219 kJ/kg.^{o}Cat 100^{o}C)

h_{2}= enthalpy of return water (kJ/kg)

ρ= density of water at pump (kg/m^{3}) (1000 kg/m^{3}at 5^{o}C, 958kg/m^{3}at 100^{o}C)

For low pressure pumped circulation systems - LPHW (3) can be aproximated to

Q = H / 4.185 (t_{1}-t_{2})(3b)

where

t_{1}= flow temperature (^{o}C)

t_{2}= return temperature (^{o}C)

For low pressure pumped circulation systems - LPHW a head *10 to 60 kN/m ^{2}* and major pipe friction resistance of

*80 to 250 N/m*per meter pipe is common.

^{2}For high pressure pumped circulation systems - HPHW a head *60 to 250 kN/m ^{2}* and major pipe friction resistance of

*100 to 300 N/m*per m pipe is common.

^{2}

The circulating force in a gravity system can be calculated as

p = h g (ρ_{1}- ρ_{2})(4)

where

p = circulating pressure available (N/m^{2})

h = height between center of boiler and center of radiator (m)

g = acceleration of gravity = 9.81 (m/s^{2})

ρ_{1}= density of water at flow temperature (kg/m^{3})

ρ_{2}= density of water at return temperature (kg/m^{3})

### 5. Sizing Pipes

The total pressure loss in a hot water piping system can bed expressed as

p_{t}= p_{1}+ p_{2}(5)

where

p_{t}= total pressure loss in the system (N/m^{2})

p_{1}= major pressure loss due to friction ( N/m^{2})

p_{2}= minor pressure loss due to fittings ( N/m^{2})

The major pressure loss due to friction may alternatively be expressed as

p_{1}= i l(6)

where

i= major pipe friction resistance per length of pipe (N/m^{2}per meter pipe)

l= length of pipe (m)

Friction resistance values for the actual pipes and volume flows may be obtained from the special charts made for the pipes or tubes.

Minor pressure loss due to fittings as bends, elbows, valves and similar may be calculated as:

p_{2}= ξ 1/2 ρ v^{2}(7)

or as expressed as "head"

h_{loss}= ξ v^{2}/ 2 g(7b)

where

ξ= minor loss coefficient

p_{loss}= pressure loss (Pa (N/m^{2}), psi (lb/ft^{2}))

ρ= density (kg/m^{3}, slugs/ft^{3})

v= flow velocity (m/s, ft/s)

h_{loss}= head loss (m, ft)

g= acceleration of gravity (m/s^{2}, ft/s^{2})

### 6. The Expansion Tank

When a fluid heats up it expands. The expansion of water heated from *7 ^{o}C to 100^{o}C* is approximately

*4%*. To avoid the expansion building up a pressure in the system exceeding the design pressure, it is common to led the expanding fluid to a tank - open or or closed.

#### Open expansion tank

An open expansion tank is only relevant for Low Pressured Hot Water - LPHW - systems. The pressure is limited by the highest location of the tank.

The volume of an open expansion tank should be the double of the estimated expansion volume in the system. The formula below can be used for a hot water system heated from *7 ^{o}C to 100^{o}C (4%):*

V_{t}= 2 0.04 V_{w}(8)

where

V_{t}= volume of expansion tank (m^{3})

V_{w}= volume of water in the system (m^{3})

#### Closed expansion tank

In an closed expansion tank the pressure in the system is maintained partly by compressed air. The expansion tank volume can be expressed as:

V_{t}= V_{e}p_{w}/ (p_{w}- p_{i})(8b)

where

V_{t}= volume of expansion tank (m^{3})

V_{e}= volume by which water contents expands (m^{3})

p_{w}= absolute pressure of tank at working temperature - operating system (kN/m^{2})

p_{i}= absolute pressure of cold tank at filling - non operating system (kN/m^{2})

The expanding volume may be expressed as:

V_{e}= V_{w}(ρ_{i}- ρ_{w}) / ρ_{w}(8c)

where

V_{w}= volume of water in the system (m^{3})

ρ_{i}= density of cold water at filling temperature (kg/m^{3})

ρ_{w}= density of water at working temperature (kg/m^{3})

The working pressure of the system - *p*_{w} - should be so that the working pressure at highest point of the system corresponds to the boiling point 10^{o}C above the working temperature.

p_{w}= working pressure at highest point

+ static pressure difference between highest point and tank

+/- pump pressure (+/- according the position of the pump)

### 7. Selecting Safety Valves

#### Safety valves for forced circulation (pump) systems

Safety valve settings = pressure on outlet side of pump + 70 kN/m^{2}

#### Safety valves for gravity circulation systems

Safety valve settings = pressure in system + 15 kN/m^{2}

To prevent leakage due to shocks in the system, it is common that the setting is no less than *240 kN/m ^{2}.*

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