Asteel sphere (sg = 7.8) of 13 mm diameter falls at a constant velocity of 0.6 m/s through an oil (sg = 0.90). calculate the viscosity of the oil assuming that the fall occurs in a large tank and that the reynolds number is very small.

1.058 decapoise

Explanation:

The specific gravity of a substance is equal to the density of substance in CGS system and if the specific gravity is multiplied by 1000 then we get the density of substance in MKS system.

Density of steel, ρ = 7800 kg/m^3

density of oil, σ = 900 kg/m^3

v = 0.6 m/s

diameter = 13 mm

radius, r = 6.5 mm

Let η be the coefficient of viscosity.

Use the formula for the terminal velocity

η = 1.058 decapoise

the area between the graph and the t axis

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.