54 
PROFESSOR E. C4. COKER AND MR. S. B. CLEMENT ON THE VARIATION 
motion was eddy or sinuous. The correction factor to ’oe applied may be obtained as 
follows :— 
If we assume that in stream-line motioji or sinuous motion the total resistance i 
depends on powers of the pipe I'adius, the kinematic viscosity, the density and the 
velocity, we may write, vcith the usual notation, 
i — 
where r = radius of the pipe, 
V = coefficient of kinematic viscosity, 
p = density, 
V = mean velocity of water along the pipe, 
h = a constant. 
Dimensionally this equation becomes 
[giving the relations 
and therefore 
[M] [L] 
[D1 
y 
DF 
- 
~r 
T _ 
_L'b 
T_ 
2y -- 3^ + n = 1, 
y-\-n 
— o 
hp 
For the case of stream-line motion, n = 1 oivinar 
i = hprw. 
For the case of sinuous motion is greater than unity, and we may write the 
equation 
p r’'v'‘ 
= Kp- "p'* \ where K = 
Taking logarithms, we get 
log ^ = log K + (2 — n) log p + (n — 1) log p. 
Ditferentiating with v coiistant, we olRain 
1 di 
t dr 
Now p = 
+ OLT I3t~ 
approximately, therefore 
therefore 
1 da 
jjb dr 
1 (la 
p dr 
+ in 
p dr 
(a + 2/3t) 
1 + 
and p = Pq (I — yt) 
