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2.1 Fluids and Flow.
A fluid is defined as any substance that can flow. This is usually a gas or a liquid as solids made of tiny particles can flow.
Density is a measure of the mass per unit volume of a material and measured in kg m3. The formula is:
An object in a fluid experiences and upwards force caused by fluid pressure called upthrust. Archimedes Principle states that upthrust is equal
to the weight of the fluid displaced by the object. The formula is:
Where V is the volume of the fluid displaced and g is the acceleration due to gravity.
We can work out if an object sinks by working out the resultant force of upthrust and weight. Weight is:
As an object sinks deeper, the force of upthrust is greater. When upthrust and weight are equal, the object will float. Therefore, in order to float,
an object must sink until it has displaced the equivalent amount of fluid to its weight.
Laminar flow describes how a fluid moves in layers and in each layer, the fluid moves at the same velocity over time. The lines/layers or laminar
flow are called streamlines. Streamline flow creates low amounts of drag.
In turbulent flow, the velocity at any one given point changes over time. The flow becomes chaotic and eddies are created. Turbulent flow
The principle of aerodynamics is to change the shape of an object in order to create laminar flow.
The friction acting against movement through a fluid is called viscous drag. This frictional force is caused by viscosity. If there is low drag,
viscosity is low. (eta) is the symbol for the coefficient (measure) of viscosity.
The rate of flow of a fluid through a pipe is inversely proportional to the viscosity. As one gets bigger the other gets smaller. The viscosity
of a fluid determines the frictional force within a fluid.
In general, fluids have a lower coefficient of viscosity at higher temperatures. For gases, viscosity increases with temperature.
Stokes law can be used to calculate the viscous drag (F) on a spherical object:
Where r is the radius (m) is the viscosity (Pas) or (kg m2) and v is the velocity (ms1).
We can calculate the terminal velocity (from stokes law) as we know that:
If we insert the equations:
We can cancel out , r and the units to give:
This is the formula used to calculate terminal velocity. The formula shows that terminal velocity is directly proportional to the radius.
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