Mechanical Properties of Fluids

A fluid is a substance that can flow and does not resist a shear stress indefinitely.

The pressure at a point in a static fluid has the same value in all directions.

The SI unit of pressure is newton metre.

In a static fluid of uniform density, pressure increases linearly with depth measured from the free surface.

Pascal’s law states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and the walls of the container.

A hydraulic lift can multiply force, but it cannot multiply energy.

For a completely submerged body, the buoyant force always acts through the geometric centre of the body.

Archimedes’ principle states that the loss in weight of a body immersed in a fluid equals the weight of the fluid displaced.

A body floats in a liquid if its average density is greater than the density of the liquid.

In a steady (streamline) flow, the velocity of each fluid particle at a given point does not change with time.

Two streamlines can intersect each other at a point in an ideal steady flow.

The equation of continuity expresses conservation of mass for an incompressible fluid in steady flow.

According to Bernoulli’s equation for an ideal fluid, if the speed of flow increases along a streamline, the pressure must also increase.

In horizontal flow of an ideal fluid through a constriction, the fluid speed is higher and the pressure is lower in the narrow section than in the wide section.

Viscosity is a measure of internal friction in a fluid, and it tends to oppose relative motion between adjacent layers.

For a Newtonian liquid in laminar flow between parallel plates, the shear stress is proportional to the velocity gradient perpendicular to the flow.

Reynolds number is a dimensionless quantity that helps predict whether a flow will be laminar or turbulent.

Very high Reynolds number generally indicates laminar flow in a pipe.

Stokes’ law for the viscous drag on a small sphere moving slowly through a viscous fluid is valid when the flow around the sphere is turbulent.

For a small sphere falling through a viscous liquid, the terminal velocity is reached when the net force on the sphere becomes zero.

Surface tension of a liquid is defined as the force per unit length acting along the surface, perpendicular to a line drawn in the surface.

For a liquid that wets the walls (like water in clean glass), the capillary rise increases when the radius of the capillary tube is increased.

The excess pressure inside a soap bubble of radius \(R\) is twice that inside a liquid drop of the same radius made of the same liquid.

In applying Bernoulli’s equation between two points in a real fluid flow, viscous energy losses are often accounted for by including an effective pressure or head loss term.

In dimensional analysis of viscous flow past a sphere, if drag force \(F\) depends on fluid density \(\rho\), viscosity \(\eta\), sphere radius \(r\) and speed \(v\), then at low Reynolds number the drag coefficient is effectively independent of \(\rho\) and \(v\).