explain how the kink in the characteristics as due to secondary emission from the anode
Secondary emission Secondary emission can be undesirable such as in the tetrode thermionic valve (tube). In this instance the positively charged screen grid can accelerate the electron stream sufficiently to cause secondary emission at the anode (plate). This can give rise to excessive screen grid current. It is also partly responsible for this type of valve (tube), particularly early types with anodes not treated to reduce secondary emission, exhibiting a 'negative resistance' characteristic, which could cause the tube to become unstable. This side effect could be put to use by using some older valves (e.g., type 77 pentode) as dynatron oscillators. This effect was prevented by adding a third grid to the tetrode, called the suppressor grid, to repel the electrons back toward the plate. This tube was called the pentode.
Fanning friction factor This friction factor is one-fourth of the Darcy friction factor, so attention must be paid to note which one of these is meant in the "friction factor" chart or equation consulted. Of the two, the Fanning friction factor is the more commonly used by chemical engineers and those following the British convention.