1277 
23-. The boundary D, and the boundary conditions on it 
having been fixed, one can solve the equations (14.4) and (14.5) 
x Fig. 11 in M. Here numerical integra- 
Me D tion shows that it 1s accurate 
M 
enough to assume that the 
characteristics of Q are 
CHARACTERISTIC 
Or . 
are Q straight. Now the actual. slope 
t of a Q characteristic is c = u. 
ss Let the assumed constant slope 
be -A, which is defined as follows: 
2A = (cou), + (c-u)) (23.1 
where the points a and b are shown in fig. 11. One then finds 
(emu), = ep = Aa, - Ka a,, , 
and by (22.11) (c-u), = a2 Ie Ya, = X=2a, + haa oe 
Hence A= a Gan wel Qa (23.2 
Then the equation of a characteristic passing through (0, ty) 
is 
x =A (t, - t), (23.3 
where A is given by the preceding equation (23.2). 
24. One may now find Qy as a function of tye To do this 
it is convenient to regard te as the independent variable. The 
relationship between Q, and t, is then given by sue parametric 
equations: 
Q® = 45 + ate + dota” (24.1 
A (t,) 
according to (22.7) and (23.3), where, 
25 
