Answer :
2. The pressure at a point in a fluid is the same in all directions.
3. The dynamic viscosity of the oil is 0.0287 poise, and the kinematic viscosity of the oil is 3.02 × 10⁻⁵ stokes.
2: Pressure at a point is the same in all directions
The pressure at a point is the same in all directions, meaning that the pressure applied to a surface is perpendicular to the surface, but the pressure applied to a liquid in a container is the same at all points.
The force applied on the liquid is proportional to the pressure exerted on the surface.
The reason the pressure is the same in all directions is due to the molecules in the fluid transferring force equally throughout the fluid.
The pressure at a point in a fluid is the same in all directions.
3: Calculation of dynamic viscosity and kinematic viscosity of oil
The given variables are:
Side of plate = 60 cm
= 0.60 m
Thickness of oil film = 12.5 mm
= 0.0125 m
Velocity of upper plate = 2.5 m/s
Force applied to maintain the speed = 98.1 N
Specific gravity of oil = 0.95
Using Newton's law of viscosity, we can write that the force required to move the fluid in between the plates,
F is given by:
F = A(η(dv/dy))
where,
A is the area of the plateη is the viscosity of the fluid,
dv/dy is the velocity gradient
As the distance between the plates,
d is much smaller than the length and breadth of the plate,
we can assume that the flow is laminar.
In laminar flow, dv/dy = v/d
Where, v is the velocity of the oil, and
d is the thickness of the oil film.
Substituting the given values in the formula and solving for dynamic viscosity,
we get
η = Fd² / (8Av)η
= 98.1 × 0.0125² / (8 × 0.6 × 0.60 × 2.5)η
= 0.0287 poise
The density of oil is given by 0.95 × 1000 kg/m³
= 950 kg/m³.
The kinematic viscosity of oil can be calculated as:
ν = η / ρν
= 0.0287 / 950ν
= 3.02 × 10⁻⁵ stokes
Therefore, the dynamic viscosity of the oil is 0.0287 poise, and the kinematic viscosity of the oil is 3.02 × 10⁻⁵ stokes.
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