Archimedes Principle In Physics

Background and History

Archimedes’ Principle

Archimedes’ Principle saied that when a body immersed in a liquid it will has an upward force equal to the weight of fluid displaced. In order to float, the volume of the vessel below the water it will displace a weight of liquid equal to the total weight of the vessel. The upward force produced by the displacement of water is termed buoyancy or displacement, and is given the symbol ‘FB’ in Figure below.

Bernoulli Principle

The term hydrodynamics was introduced by Daniel Bernoulli (1700-1783), the man who also discovered the fundamental theorem relating velocity, pressure, and elevation for the steady, frictionless flow of an incompressible fluid along a given streamline (Gillmer

C., 1970, p. 158)

Reynolds Number

Sir Osborne Reynolds conducted a series of experiments on the factors controlling the pressure drop in pipes .

Experiment pipe-flow apparatus of Osborne Reynolds (Gillmer & Johnson, 1932, p. 215)

At low velocity, the dye filament remained stable and the flow appeared to move smoothly along streamline layers parallel to the walls with maximum velocity at the centre of the pipe

(Figure 4). This was called laminar flow. (Gillmer & Johnson, 1932). In a laminar flow, when the water is moving past the hull at low speed, a smooth flow can be observed. In this flow the molecules of water are flowing past the hull one behind the other in a single file (Hamlin,

1989, p. 50).

Laminar velocity profile in a pipe (Gillmer & Johnson, 1932, p. 215)

When Reynolds increased the flow rate through the tube, the dye streaks were observed to become sinuous, the unstable, and finally the whole flow became mixed with unobservable dye streaks (Figure 5). This type of flow is called turbulent (Gillmer & Johnson, 1932, p.

214). In a turbulent flow when a ship is travelling at high speed in smooth water, it can be observed that the water closest to the hull is being dragged along at nearly the speed of

In fact the molecules of water touching the hull are moving exactly with the hull (Hamlin, 1989, p. 49).

Turbulent velocity profile in a pipe (Gillmer & Johnson, 1932, p. 215)

By changing the diameters of the tubes, the flow rate, and the fluid kinematic viscosity, he was able to determine that the breakdown of the laminar flow into turbulence appeared to depend on a dimensionless combination of these variables that equalled approximately 2000, unless great care was taken not to disturb the incoming flow.

Rn (critical)=PuD/µ≈ 2000

u = Average fluid velocity D = Pipe diameter µ = Dynamic viscosity of fluid

The critical Reynolds number of about 2000 defines when transition from laminar to turbulent flow may being for internal pipe flow (Gillmer & Johnson, 1932, pp. 214-215).

In simple terms, laminar flow is where viscous forces predominate and a turbulent flow is where viscous forces are overtaken by inertia forces. Reynolds number is the key indicator of the type of flow and when it reaches a value of 4.5 x 105 for ships it is found that the flow becomes unstable and is leaving the laminar region (Gillmer T. C., 1970, pp.