1913-14.] Viscous Flow through a Circular Tube. 
63 
Tube B. 
Loss of head in cm. 
Experiment. 
Total. 
In viscous 
resistance. 
Due to T 
at outlet. 
Besidue 
K> 
V 
c. per sec. 
v 2 
w 
1c. 
1 
16-02 
8-155 
1-000 
6-865 
69-60 
2-470 
2-78 
2 
16-64 
8-390 
55 
7-250 
71-30 
2-595 
2-80 
3 
12-56 
6-905 
55 
4655 
58-75 
1-760 
2-65 
4 
11-81 
6-550 
55 
4-260 
55*70 
1-581 
2-69 
5 
7-50 
4-501 
55 
1-999 
38-23 
0-745 
2-68 
6 
7-46 
4-490 
55 
1-970 
38-20 
0-744 
Mean = 
2-65 
2-71 
Tube C. 
1 
16-90 
11-98 
0-57 
4-35 
57-90 
1-705 
2-55 
2 
16-60 
11-85 
55 
4-18 
56-90 
1-646 
2-54 
3 
12-43 
9-30 
55 
2-56 
44-65 
1-015 
2-53 
4 
12-55 
936 
55 
2*62 
44-95 
1-029 
2-54 
Mean = 
2-54 
From these results it appears that the sum of the residual losses is 
between 2*5 and 3*0 times — . Of this, the kinetic energy of discharge 
accounts for 2~. The remainder, incurred at entry to the tube, is equal 
* 9 
to Ctz- , where c has mean values as follow : — 
2g 
Ratio 
outer diameter 
1-33 
1-50 
3-50 
inner 
(=m) 
Mean value of c 
•71 
•65 
•54 
1 
2 - V 
•70 
•64 
•52 
m 2 
The value of c appears to increase slightly with an increase in speed. 
Its mean values over the range of values of m occurring in the experi- 
ments are given with fair accuracy by the relationship 
and as this also satisfies the two extreme conditions, i.e. makes c = 1 when 
m=l, as in a thin- walled tube, and makes c — m 5 when m is very large, 
values calculated by this relationship are probably fairly accurate for all 
intermediate values of m. 
(. Issued separately February 19, 1914.) 
