Building Services Engineering 5th Edition Handbook

212 Soil and waste systems
The intended conditions are:
and,
G = 0.15
16 = 0.009375
L = 16 + 5 = 21 m
Using L/G = 35 2 for an equivalent length of 21 m the gradient cannot be less than:
G =
L
35 2
= 21
35 2
= 0.01714
The intended gradient is less than the minimum allowable gradient and so the design must be
modified.
Assuming that the WC can be brought nearer to the stack, how far away can it be? There are
two conditions to be met:
G = 0.15
L
(7.1)
L + 5
G = 352 (7.2)
Substitute equation (7.1) into equation (7.2) to eliminate G:
(L + 5) × L
0.15 = 352
This can be rearranged to:
L 2 + 5L = 183.75
L 2 + 5L − 183.75 = 0
This is a standard quadratic equation of the form,
ax 2 + bx + c = 0
where x = L, a = 1, b = 5 and c =−183.75. The solution of the quadratic is:
x = −b ± √ (b 2 − 4ac)
2a