\.\ii COMPUTATION ftULES. 



Example 10. The crashing load of a hollow, cast-iron pillar of circular 

 section, with concentric surfaces of diameters D and d as given by Hodgkinson 

 (Lanza, "Applied Mechanics, 1 ' pain.- 332) is 



T (Z> 2 -'?-') 

 C=I0980I 



Desired to ten per cent the load which a pillar of external and internal diame- 

 ters 4.032 iiiclu-s and 2.16 inches, respectively, would carry. How many places 

 of figuivs should be used in the computation ? 



Ten per cent results call for three figures in all factors (page xiii). The 

 factors in this expression are 109 801, ?r, (D- d 2 ), and 4, each of which 

 should therefore be carried to three figures. The first two should therefore be 

 1 10 ooo and 3. 14. The 4 is a complete number as it stands. D- d 2 = 4.0- 2.2 2 

 roughly = 1 6.0 4.8 = 11.2. To have three figures, it should therefore be car- 

 ried to the first decimal place. Then as it is made up of two quantities, one 

 subtracted from the other, each of these should be carried (page xiv) to the 

 decimal place desired in the result, i.e. to the tenths' place. This requires D 2 

 to contain three figures, 16.0, and hence D should contain three figures (since 

 D 2 consists of the factors DxD),i.e. should be written 4.03 inches. The require- 

 ment of one decimal place in cP calls for but two figures, 4.8, and hence two 

 figures, 2. 2 inches, in d. The numerical expression to be solved would then be 



3. 14(4.O3 2 2.2 2 ) 



c = 110 ooo^- -, 



which would be most easily worked by a simple slide rule, or by direct multipli- 

 cation. 



Example 11. Desired to o. i per cent the fraction of dry steam in a 

 sample of steam, using the following observations made with the "Barrus 

 Calorimeter" (Peabody's " Themodynamics of the Steam Engine," page 234), 

 the formula being 



_ W(q z - qi) + e-w(q- g 3 ) 

 wr "~~ 1 



where 



x = fraction of a mixture which is dry steam ...... 



W = weight of cooling water ........... 5735 H>s. 



w = weight of condensed water .......... 29.89 Ibs. 



t temperature of steam ............ 



t\ = initial temperature of cooling water ....... 37-49 F. 



f-2 = final temperature of cooling water ........ 83. 84 F. 



t-i = temperature of condensed water ........ 304- 88 F. 



</ 3 = "heat of liquid" at 3 , from 3 and tables ..... 274.4 



r/ 2 = "heat of liquid" at 2 , from t z and tables ..... 51.91 B. T. U. 



Vi = " heat of liquid " at i, from ti and tables ..... 5.53 B. T. U. 



7 = "heat of liquid" at <, from t and tables ..... 287.6 B. T. U. 



e = radiation loss during test ........... 120. B. T. U. 



r = latent heat of steam at , from tables ...... 891.2 B.T.U. 



What number of places of figures should be used throughout ? 



Solution. For o. i per cent the result, and therefore all factors, should 

 have five places of figures (page xiii). The only factors of the whole expression 



