## Back to basics: Help me deepen my theoretical understanding of designing a system

Hey everyone,

I would like to broaden my theoretical understanding by using an simplified example:

There is a building containing one room with a floor surface of 40 m2 which needs exactly 2.8 kWs to maintain its room temperature while outside temp is -10 celcius (The heat-loss of the house is 70 Watt / m2 at -10 degrees celcius).

 The room is heated by a floor-heating-system which has double the capacity to heat the room. It has 5.6 kWs of heating capacity.
 The distance between the heat source(a traditional naturalgasburing heatsource) and the floor heating dispenser is 20 meters.
 For this exercise i want to assume there is 0% friction in the piping. The piping is straight and leveled.
 The pressure that the heat-source can exert on the water by means of a pump is limitless.
 The speed of the water may never exceed 1 m/s
 The water temperature is 35 degrees Celsius.
 The goal is to maintain a delta T of 5 degrees Celcius. This the temperature of the returning water should be 30 degrees.

Given the above stated facts what should be the minimum diameter of the pipes? Can you please show the formula by which this can be calculated?

___

I'll give it a try myself.
To determine the diameter we first need to determine the flow that is needed to meet our quota of 2.8 kW's. The formula to determine that is:
Q = kW / 4.18 x Delta T

2.8 kw / ( 4.18 x 5 degrees celcius) = 0.13kg /s

0.1339 x 3.6 = 0.4823 m3/h

Q = 0.48 m3/h

If this formula is correct. Than where does the 4.18 come from?

Now based on Q and the maxium allowed speed of 1 m/s i can calculate:

Q / 3600 / maximum allowed speed*4) / PI^0.5 = 0,0131 m x 1000 = 13,1 mm.

Tell me am i or is it 