Tag: physics

The viscous drag force can be written as below:
$F =  \eta \ A \ (\cfrac{dV}{dX})$ where, F is viscous drag force (or tangential force)
$\eta$ is coefficient of viscosity
$A$ is surface area of layers in contact
$\dfrac{dV}{dX} $ is velocity gradient
$\eta$ is property of liquid.
So, we can see that drag is directly proportional to the velocity gradient, surface area and nature of liquid. Drag force acts in opposite direction of liquid flow. 

A fluid that has no resistance to shear stress between its layers is known as an ideal fluid.(Definition).Hence ideal fluid  has zero viscosity.

Viscosity depends of mass of body, temperature, velocity and density.
Where as friction depends only on normal reaction.

According to Stokes' Law, the viscous drag force F on a sphere of radius R moving at velocity v in a fluid is given by F = 6 * pi * eta * R * v. Thus, the force is directly proportional to the radius R.

Due to surface tension of oil capillary rise can be seen in cotton wick which makes lamp to burn.

The equation of motion for a falling sphere is m*a = mg - F_buoyant - F_viscous. At terminal velocity v_t, the net force is zero, so F_viscous = mg - F_buoyant. When v = v_t/3, the viscous force is F_viscous' = (1/3) * F_viscous. Substituting this, the acceleration becomes a' = (1 - 1/3) * g_effective = (2/3) * a_initial. The question asks for a/X, where a' = a/3, implying X=3.

If angle of contact is acute, liquid rises in a capillary tube whereas if angle of contact is obtuse, liquid is depressed in a capillary tube.

Terminal velocity v_t is proportional to r^2. The drag force F = 6 * pi * eta * r * v_t. Substituting v_t proportional to r^2, we get F proportional to r * r^2 = r^3. The ratio of forces for radii r and 2r is (r/2r)^3 = 1/8.

The rate at which a stirred liquid comes to rest depends on its viscosity. Glycerine has the highest viscosity among the given liquids, causing it to dissipate kinetic energy through internal friction most rapidly.