802 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
AM)= P U-^, 
^(M)=pv y 
' u \ r , pa? S dpa U S dpa? 
<r,(M u) = p -r~-r_ - p - 
Q ''V 
4 y/1 t dx 4 dx ’ 
“/Ti/r \ P* 2 s dp«U L s dpa 2 I 
,(M«)= j—^ —+g ^-.J 
>■ 
^(M“)=+fA- 
s 
dpa U 
S dpa 3 
s 
2y/7T 
dy 
27 r dx 
1 
04 
1 
S 
dpaU 
S dpa 2 
s 
2^/7 T 
dy 
27t dx 
2-y/ 7T 
(43) 
(44) 
(45) 
<T,(Mm) = 
tr J (M«)= — 
pa 3 2s dpaU 
2 y/V dx ’ 
s dpaV s dpaU . 
■y/7T dx y/lT dy ’ ■ 
/1>r . s dpaW s dpaU 
^ Mm =-7- — — -7- » 
V ' <y/ IT dx \y 7T fife 
with corresponding equation for Q=M v, Q = Mw, 
3s d pa. 
<r,{M(tt*+ v*+w*)} = |pa^U- —- ^ 
and similar equations. 
(46) 
(47) 
The values of U, V, W. 
Hitherto U, V, W have been treated merely as functions of x, y, z. They are, how¬ 
ever, completely expressed by equation (43). 
For remembering that cr f (M), cr y (M), cr ; (M) are respectively equivalent to pu, pv, piv, 
we have 
U =u 
Y=v 
hY-w 
S dpa ^ 
•y/ irp dx ’ 
S d pa. 
s/trp dy ’ | 
s dpa } 
v irp dz J 
(48) 
