1.how does coefficient of viscosity depend on temperature?2.a piece of wood is taken deep inside a long column of watern and released.why willpiece of wood move up with a decreasing upward acceleration?3why is there no terminal velocity in vaccum

1.coeff of viscosity in liquids dec with inc in temp.for gases it inc with inc in temp

is there any mathematical relation between coefficient of viscosity and temperature

A1) The coefficient of viscosity of liquids decreases with increase in temperature and relation is of exponential decrease with temperature. A2) The wood experiences upthrust that is more than its weight so there will be acceleration of the wood upwards.But the viscous force of water will act on the wood opposite to this motion that is in the downward direction.This viscous force is directly proportional to the velocity of the moving object.So as the velocity of the wood increases because of net acceleration upwards, the viscous force in the downward direction will also increase so the net upward force will be continuosly decreasing and therefore the acceleration will also be decreasing. A3 )As there is no fluid in vaccum no viscous force acts on a body in vaccum.The viscous force is directly proportional to the velocity of the moving object , and if the velocity is increasing there may be a point when the viscous force becomes equal to the net forward force on the object and at that point the net force becomes zero on the body and it moves with constant velocity ,ie , terminal velocity .This cant take place in vaccum.