Page:Steam heating and ventilation (IA steamheatingvent00monrrich).pdf/55

Figure 26.—Diagram of Indirect Apparatus.

foot of a gas of any temperature is inversely proportional to its absolute temperature, which is the temperature in degrees Fahrenheit + 460, or $W=c\div (t+460)\,$, where $W\,$ is the weight per cubic foot, $t\,$ the temperature in degrees Fahrenheit, and $c\,$ a constant, different for each gas and which, for air, equals approximately 40. If t be the temperature of the cold air and $T\,$ be that of the air in $D\,$, then the pressure per square foot due to a column of cold air of height $H\,$ feet would be $p=40H\div (t+460)\,$ and the pressure due to a column of hot air of the same height would be $P=40H\div (T+460)\,$. The difference of pressure which creates the flow of air then is

$p={\dfrac {40H}{t+460}}-{\dfrac {40H}{T+460}}={\dfrac {40H(T-t)}{(t+460)(T+460)}}$

The head, $h\,$, which creates the velocity of flow, is equal to the height of a column of air of temperature $T\,$ which would give the pressure $p\,$, or

$h={\dfrac {p(T+460)}{40}}={\dfrac {H(T-t)}{t+460}}$

By the laws governing the flow of fluids the theoretical velocity