Let _a_ = difference between the two assumed diameters. _b_ =
increase found over lower diameter. _c_ = decrease found under
greater diameter. _d_ = lower assumed diameter.


Then true diameter =

[*Math: d + \frac{ab}{b+c} = 30 + \frac{10 \times
4.64}{4.64+0.06} = 30 + \frac{46.4}{4.7} = 39.872],

or, say, 40 in, which equals the required diameter.

A simpler way of arriving at the size would be to calculate it
by Santo Crimp's formula for sewer discharge, namely, velocity
in feet per second =

[*Math: 124 \sqrt[3]{R^2} \sqrt{S}],

where R equals hydraulic mean depth in feet, and S = the ratio
of fall to length; the fall being taken as the difference in
level between the sewage and the sea after allowance has been
made for the differing densities. In this case the fall is
20.42 ft in a length of 6,126 ft, which gives a gradient of 1
in 300. The hydraulic mean depth equals

[*Math: \frac{d}{4}];

the required discharge, 2,497 cubic feet per min, equals the
area,