w = (U2 + V2) a2 z+ a2b2 U + Vi
b2 − a2 U + Vib2 − a2 z
−(U12 + V12) b2 z− a2b2 U1 + V1i.
b2 − a2 U1 + V1ib2 − a2 z

(19)

The resultant impulse of the liquid on the cylinder is given by the component, over r = a (§ 36),

X = ∫ ρφ cos θ·a dθ = πρa2 ( U b2 + a2− U1 2b2);
b2 − a2 b2 − a2

(20)

and over r = b

X1 = ∫ ρφ cos θ·b dθ = πρb2 ( U 2a2− U1 b2 + a2),
b2 − a2 b2 − a2

(21)

and the difference X − X1 is the component momentum of the liquid in the interspace; with similar expressions for Y and Y1.