APPENDIX A

297

the hydrostatic head when the flow in opposite directions is
carried out at the same manometer pressure p. Let the time of
flow in the one direction tL, under the true pressure corrected for
hydrostatic head PL = p + hip, be supposed to be less than the
time tR in the opposite direction under the pressure PR = p
— &ip. Then

^

and substituting into this equation the values of pL and p& given
by Eq. (1), we have

i, 1 h + CWfc v + CrP/tR\
ni ~ 2p\ CtL CtR I

but in the kinetic energy correction, which is itself always small,
the small hydrostatic head correction is of negligible influence,
hence for our purpose we may write 77 + C'p/tL = -r\ + C'p/tR so

hl =='

(6)

but from Eq. (1) we have that 17 + C'p/tL = CpLtL
hence

, = Pi *R ~ ^
2p IR

THE TRUE AVERAGE PRESSURE

It might inadvertently be assumed that if the two bulbs C and
K are the same in shape and volume and also at the same level,
the true pressure to be used in calculating the viscosity would
necessarily be the pressure pi delivered by the compressed air in
the viscometer because the hydrostatic head as obtained above
would then be zero. But since the hydrostatic head in the vis-
cometer is really continually changing, the true average pressure
may not be zero under the above conditions, and it must be
obtained by integration. Bingham, Schlesinger, and Coleman
(1916)1 have shown that for cylindrical bulbs the true average
pressure p would be

0.8686/ip

p =-

logio

po

(7)

po —

1 For other shapes of bulbs see original paper of Bingham, Schlesinger,
and Coleman. For the possible importance of such corrections see Kendall
and Munroe (1917).