Mechanical Properties Of Fluids

Newton's Law of Viscosity states that for a streamline flow of a fluid, the viscous force ( ) acting between two adjacent layers is directly proportional to the area of the layers ( ) and the velocity gradient ( ) between them. Introducing a constant of proportionality, , we get: The negative sign indicates that the viscous force opposes the relative motion between the layers. The constant is called the coefficient of viscosity.
Derivation of the Expression for :
From the formula above, we can rearrange the terms to solve for the coefficient of viscosity, . Considering only the magnitude of the force: This is the expression for the coefficient of viscosity.
is the tangential viscous force.
is the area of the layer.
is the velocity gradient, which is the rate of change of velocity with distance perpendicular to the direction of flow.
The SI unit of the coefficient of viscosity is Pascal-second (Pa·s) or N·s/m².

Bernoulli's theorem is a statement of the principle of conservation of energy for a flowing fluid. It states that for an ideal fluid in steady flow, the sum of its pressure energy, kinetic energy per unit volume, and potential energy per unit volume remains constant along a streamline. Therefore, it is the total energy of the fluid that is conserved.

The surface tension of a liquid becomes zero at its critical temperature. At this temperature, the distinction between the liquid and gas phases disappears, and the intermolecular cohesive forces that cause surface tension become negligible.

First, we calculate the excess pressure ( ) inside the water drop due to surface tension. The formula for a liquid drop is: We need to convert the given values to SI units.
Diameter = 0.6 mm, so radius
Surface tension, .
Since and ,

Now, calculate the excess pressure: The total pressure inside the drop ( ) is the sum of the atmospheric pressure ( ) and the excess pressure. The pressure inside the water drop is N/m .