Whena viscousliquid flows , adjacentlayersopposetheir relativemotion by applyinga viscousforcegiven by F = - eta A (dv)/(dz) where , ete= coefficientof viscosity, A = surface areaof adjacentlayers in contact, (dv)/(dz) = velocity gradient Now , a viscous liquid havingcoefficient of viscosityetais flowingthrough a fixedtube of lengthl and radiusR undera pressure difference P between the two ends of the tube . Nowconsider a cylindrical vloumeof liquidof radius r . Dueto steadyflow ,net forceon the liquidincylindricalvloumeshouldbe zero .- eta 2pirl (dv)/(dr) = Ppir^(2) - int _(v)^(0),dv = P/(2 eta l) int_(tau)^(R) rdr( :'layerin contactwith the tube is stationary )v = v_(0)(1- (r^(2))/(R^(2))), wherev_(0) = (PR^(2))/(4nl):."" Q = (piPR^(4))/(8sta l) Thisis calledPoisecuille'sequation . The volumeof the liquid flowing per secacross the cross - section of the tubeis .