50 FLUIDITY AMD PLASTICITY

and we obtain

z (l6a)

CM?7 p

or

„ -
17 ~

where Fi and ¥2 are the volumes corresponding to pressure
Pi and P2.

Since p = Pi — Pz we observe that the ratio between the

P1 _|_ p2
values of the viscosity calculated by Eqs. (17) and (5) is —^-p—

|i| [ where P may have any value between PI and ?2 depending upon

if I the value of V which is employed. If V be taken as

\W 2Pt T, _ 2P2 „

(17) becomes identical with Eq. (5) and becomes unnecessary.

The derivation of the law for gases was made by 0. E. Meyer
(1866) aad by Boussinesq (1868). With Fisher (1903) we may
regard the above case where PV is constant as extreme, and that
more generally we may take PVn as constant. Equation (16)
becomes on integration

l + i H-i

! '-Pi "

Stn

When n = <» this becomes identical with Eq* (4), for incom-
jj! pressible fluids. When n = 1 the flow is isothermal and we

obtain Eq. (16a). Ordinarily the value of n will lie between these
two extremes, thus in adiabatic expansion n = CP/CV = 1.0 to
1.7, the ratio of the specific heats. Hence, it seems probable that
the Law of Poiseuille as given in Eq. (5) may be used, irrespective
of whether the fluid is compressible or not, but in every case the
volume of flow must be taken as

l + PF!

(18)

.
Pi" +Pi» 'P, + . . .P,=
In the extreme case where n = 1, if p is not greater than P2/10