Domestic Water Heater Sizing in Excel

Domestic water heater sizing is the process of determining the right size of water heater for your home. The size of a water heater depends on several factors, such as:

• The amount and frequency of hot water you need
• The type of water heater you prefer (tank or tankless)
• The space available for installation
• The temperature of the incoming water and the desired output temperature

To size a water heater, you need to estimate the flow rate and the temperature rise for your application. The flow rate is the amount of water that flows through the water heater in a given time, measured in gallons per minute (gpm). The temperature rise is the difference between the incoming water temperature and the desired output temperature, measured in degrees Fahrenheit (°F).

To estimate the flow rate, you need to list the number of hot water devices you expect to use at any one time, such as faucets, shower heads, washing machines, and dishwashers. Then, you need to add up their flow rates to get the total flow rate. For example, if you expect to use a faucet with a flow rate of 0.75 gpm and a shower head with a flow rate of 2.5 gpm at the same time, the total flow rate is 3.25 gpm.

To estimate the temperature rise, you need to subtract the incoming water temperature from the desired output temperature. The incoming water temperature varies depending on your location and season, but you can assume it is 50°F (10°C) unless you know otherwise. The desired output temperature depends on your personal preference and the type of application, but you can assume it is 120°F (49°C) for most uses. For example, if the incoming water temperature is 50°F and the desired output temperature is 120°F, the temperature rise is 70°F.

Basic Theory:

The fundamental principle behind domestic water heater sizing is to determine the required heating capacity to meet the hot water demand of a household. The primary factors influencing sizing include the desired water temperature rise, flow rate, and the temperature of the incoming water.

Procedures:

1. Determine Flow Rate (Q): Identify the expected flow rate of hot water in gallons per minute (GPM).
2. Determine Temperature Rise (ΔT): Calculate the required temperature rise by subtracting the incoming water temperature from the desired outlet temperature.
3. Use Specific Heat Capacity (Cp): Utilize the specific heat capacity of water (4.186 J/g°C) to convert the temperature rise to energy.
4. Calculate Heating Capacity (Q = m * Cp * ΔT): The heating capacity (Q) is given by the mass flow rate (m) of water multiplied by the specific heat capacity (Cp) and the temperature rise (ΔT).

Scenario:

Let’s consider a scenario where a household requires a hot water flow rate of 3 GPM with a desired temperature rise of 30°C. The incoming water temperature is 15°C.

Excel Formulas:

1. In Excel, create a table with the following columns: Flow Rate (GPM), Temperature Rise (ΔT, °C), Specific Heat (Cp, J/g°C), and Heating Capacity (Q, Watts).
2. Input the scenario values into the corresponding cells:
   • Flow Rate (GPM): 3
   • Temperature Rise (ΔT): 30
   • Specific Heat (Cp): 4.186 (constant)
3. In the Heating Capacity column, use the formula:

   =A2 * B2 * C2 * 60

   Here, A2 is Flow Rate, B2 is Temperature Rise, C2 is Specific Heat, and the multiplication by 60 converts the result to Watts.

MATLAB Calculation:

% MATLAB code for water heater sizing
flowRate = 3; % GPM
temperatureRise = 30; % °C
specificHeat = 4.186; % J/g°C

% Convert flow rate to mass flow rate (assuming water density of 1 g/mL)
massFlowRate = flowRate * 3.78541; % LPM to LPS
massFlowRate = massFlowRate * 1000; % L to g
massFlowRate = massFlowRate / 60; % g/s

% Calculate heating capacity
heatingCapacity = massFlowRate * specificHeat * temperatureRise;

% Display the result
disp(['Heating Capacity: ' num2str(heatingCapacity) ' Watts']);

Result:

In the Excel table, the calculated Heating Capacity will be displayed in Watts. For the provided scenario, the result should be approximately 2513.1 Watts.

In MATLAB, running the code will also yield the Heating Capacity in Watts, allowing for a comparison of results between the two methods.