KEVOS® MAKEOS · Hydraulics
Hot and Cold Water Blending Check (Flow Split, Hot Supply, Entropy Generated, Lost Work)
How much hot and cold water must be blended to give a set mixed temperature and flow, can the hot supply provide it, and how much work potential is lost by mixing instead of heating to the target directly?
Adiabatic blending of a hot and a cold water stream to a target temperature: the hot share and the hot and cold flows from the energy balance, the heating power carried by the hot stream above the cold supply, the entropy generated from the entropy change of each stream as an incompressible liquid, and the lost work at the surroundings temperature, against the hot water flow the supply can deliver.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Hot supply temperature | °C | Temperature of the hot water arriving at the blending point. |
| Cold supply temperature | °C | Temperature of the cold water arriving at the blending point. |
| Target mixed temperature | °C | The mixed temperature you need at the outlet. |
| Mixed flow needed | L/min | The mixed water flow the outlets need. |
| Hot water flow available | L/min | The largest hot water flow the heater, store or supply main can deliver at the hot temperature. |
| Water and surroundings | ||
| Specific heat capacity of the water | kJ/(kg·K) | Specific heat capacity of the water (about 4.18 kJ/(kg·K) for water near room temperature). |
| Water density | kg/m³ | Density of the water. |
| Surroundings temperature for the lost work | °C | Temperature of the surroundings, taken as the dead state for the lost work. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Hot supply temperature
- What it is
- The temperature of the hot water arriving at the mixing valve or blending point, from a heater, storage tank or hot water main.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.01 °C to 99 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 65 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Hotter supply water reduces the hot flow needed and increases the entropy generated by mixing.
- Get it right
- Measure it at the blending point under flow; a long hot pipe can arrive several degrees cooler than the heater.
What this means: Cold supply temperature
- What it is
- The temperature of the cold water arriving at the blending point, from the mains or a cold water tank.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.01 °C to 99 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Colder supply water raises the hot flow needed and the heating power.
- Get it right
- Mains water temperature changes with the season; check the hot flow with the coldest winter value.
What this means: Target mixed temperature
- What it is
- The temperature the mixed water must have at the outlet of the blending point, which must lie between the cold and hot supply temperatures.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.01 °C to 99 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher target raises the hot share and the heating power.
- Get it right
- For any outlet used for washing people, check the delivery temperature limits that apply before choosing it.
What this means: Mixed flow needed
- What it is
- The total flow of mixed water the outlets need at the target temperature.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 1000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The hot and cold flows, heating power, entropy generated and lost work all rise in proportion.
- Get it right
- Use the peak simultaneous demand of the outlets, not the sum of every outlet at full flow unless they can all run at once.
What this means: Hot water flow available
- What it is
- The largest flow of hot water the heater, storage or hot main can deliver at the hot supply temperature, used as the pass or fail limit.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0 L/min to 1000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line; the flows and losses do not change.
- Get it right
- For a storage heater, check that the store can sustain the flow for the whole draw, not just the first minutes.
Water and surroundings
What this means: Specific heat capacity of the water
- What it is
- The heat needed to raise one kilogram of the water by one kelvin, used in the entropy change and the heating power.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.1 kJ/(kg·K) to 10 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.18 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The heating power, entropy generated and lost work rise in proportion; the flow split does not change.
- Get it right
- For glycol mixtures or brines use their own value, which is lower than for water.
What this means: Water density
- What it is
- The mass of one cubic metre of the water, which converts the volume flows into mass flows.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 1 kg/m³ to 2000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The heating power, entropy generated and lost work rise in proportion.
- Get it right
- Water is close to 1000 kg/m³ at room temperature and a little less when hot; brines are denser.
What this means: Surroundings temperature for the lost work
- What it is
- The temperature of the surroundings, taken as the dead state against which the work potential lost in mixing is measured.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 60 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The lost work rises in proportion to its absolute temperature.
- Get it right
- Use the ambient or cold water temperature for the site; it only scales the lost work.
Method and formulas
- Energy balance with constant specific heat: hot share f = (T_target − T_cold) ÷ (T_hot − T_cold); hot flow = f × mixed flow.
- Entropy change of an incompressible liquid ΔS = m c ln(T2 ÷ T1); entropy generated = c [ṁ_h ln(T_t ÷ T_h) + ṁ_c ln(T_t ÷ T_c)], which is positive for any real mixing.
- Lost work = T0 × entropy generated (absolute temperatures).
- Example: 30 L/min at 40 °C from 65 °C and 15 °C needs 15 L/min of each, 52.25 kW of heating; mixing generates 6.6816 W/K and loses 1.9253 kW of work at 15 °C surroundings.
Limitations
- Steady adiabatic mixing with no heat loss from pipes or the valve; constant specific heat and density.
- Temperatures at the blending point; long pipe runs lose heat before the water arrives.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the hot and cold flows of a blending station or mixing valve
- Check that a hot water supply can meet a mixed-water demand
- Show the work potential lost by storing water hotter than it is used
Who it is for
- Building services and process engineers
- Plant and maintenance engineers
- Energy auditors
What you get
- Hot share and hot and cold flows
- Heating power in the hot flow
- Entropy generated and lost work
Interpreting the result
- The lost work is the price of making hot water hotter than it is used; heating to the target directly, or using a heat exchanger, avoids most of it.
- Stored water is often kept hot for hygiene reasons, so the loss is accepted; the figure shows what that choice costs in work potential.
Before relying on the result
- Measure the hot and cold temperatures at the blending point under flow.
- Check the delivery temperature limits for any outlet used for personal hygiene.
References
- Linder, B., Thermodynamics and Introductory Statistical Mechanics (Wiley-Interscience, 2004), sections 4.11, 4.13 and 8.5, printed pp. 48–51 and 91–93: entropy change with temperature ΔS = C_P ln(T2 ÷ T1), the condensed-phase approximation and the entropy of system and surroundings. Method reference; no source text, tables or examples are reproduced.
- AS/NZS 3500.4, Plumbing and drainage: heated water services. Named for scope; it governs delivery temperatures at sanitary fixtures.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Throttling, mixing and friction
What it covers: Three losses with no heat and no visible waste: pressure regulators, tempering valves and friction in pipes and filters, their entropy generation, their cost in kilowatts and how to reduce them.
Also in Lost work and exergy
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