If, now, A is the area of the piston, then the external power (d W) produced between each ordinate is:
To any convenient scale, upon each ordinate, set off the appropriate power as calculated by this equation (1).
A(p-b)dx
dW = --------------. (1.)
33,000
There will result the curve w, w, w, determining the power which at any point in the diagram is to be regarded as a gain, to be carried to the credit side of the account.
It is evident that, so long as the gains from expansion exceed the losses from expansion, it is profitable to proceed with expansion, but that expansion should cease at that point at which gains and losses just balance each other.
TO CALCULATE THE LOSSES.
The requisite data are furnished by the experiments conducted some years since by President D.M. Greene, of Troy College, for the Bureau of Steam Engineering, U.S. Navy.
According to these experiments, the heat which is lost per hour by radiation through a metallic plate of ordinary thickness, exposed to dry air upon one side and to the source of heat upon the other, for one degree difference in temperature, is as follows:
Condition. Heat units.
Naked...................................... 2.9330672
Covered with hair felt, 0.25 inch thick.... 1.0540710
" " 0.50 " .... 0.5728647
" " 0.75 " .... 0.4124625
" " 1.00 " .... 0.3070554
" " 1.25 " .... 0.2746387
" " 1.50 " .... 0.2507097
If now t' = temperature of steam at the ordinate,
t = temperature of the surrounding atmosphere,
dS = surface of the cylinder included between each ordinate,
k = that figure from the table satisfying the conditions,
then the power loss (dR) per minute will be:
k (t'-t)dS
dR = ( -- ) ----------. (2)
60 33,000
To the same scale as the power gains, upon each ordinate, set off the appropriate power loss, as calculated by this equation (2).