Chapter 2 Review of Forces and Moments - Brown University
Chapter 2 Review of Forces and Moments - Brown University
Chapter 2 Review of Forces and Moments - Brown University
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Archimedes’ principle gives a simple way to calculate the resultant force exerted by fluid pressure on an<br />
immersed object.<br />
The magnitude <strong>of</strong> the resultant force is equal to<br />
the weight <strong>of</strong> water displaced by the object. The<br />
direction is perpendicular to the fluid surface.<br />
Thus, if the fluid has mass density ρ , <strong>and</strong> a<br />
volume V<br />
I<br />
<strong>of</strong> the object lies below the surface<br />
<strong>of</strong> the fluid, the resultant force due to fluid<br />
pressure is<br />
F<br />
Center <strong>of</strong> mass <strong>of</strong><br />
submerged portion V I<br />
= ρgV I<br />
j<br />
F<br />
Volume V I lies below<br />
fluid surface<br />
The force acts at the center <strong>of</strong> buoyancy <strong>of</strong> the immersed object. The center <strong>of</strong> buoyancy can be<br />
calculated by finding the center <strong>of</strong> mass <strong>of</strong> the displaced fluid (i.e. the center <strong>of</strong> mass <strong>of</strong> the portion <strong>of</strong> the<br />
immersed object that lies below the fluid surface).<br />
The buoyancy force acts in addition to gravity loading. If the object floats, the gravitational force is equal<br />
<strong>and</strong> opposite to the buoyancy force. The force <strong>of</strong> gravity acts (as usual) at the center <strong>of</strong> mass <strong>of</strong> the entire<br />
object.<br />
Aerodynamic lift <strong>and</strong> drag forces<br />
Engineers who design large<br />
bridges, buildings, or fast-moving<br />
terrestrial vehicles, spend much<br />
time <strong>and</strong> effort in managing aeroor<br />
hydro-dynamic forces.<br />
Hydrodynamic forces are also <strong>of</strong><br />
great interest to engineers who<br />
design bearings <strong>and</strong> car tires, since<br />
hydrodynamic forces can cause one<br />
surface to float above another, so<br />
reducing friction to very low<br />
levels.<br />
V<br />
F L<br />
(Lift acts perpendicular<br />
to flow)<br />
F D<br />
Flow is asymmetric near airfoil<br />
(Drag acts parallel<br />
to flow)<br />
In general, when air or fluid flow past an object (or equivalently, if the object moves through stationary<br />
fluid or gas), the object is subjected to two forces:<br />
1. A Drag force, which acts parallel to the direction <strong>of</strong> air or fluid flow<br />
2. A Lift force, which acts perpendicular to the direction <strong>of</strong> air or fluid flow.<br />
The forces act at a point known as the center <strong>of</strong> lift <strong>of</strong> the object – but there’s no simple way to predict<br />
where this point is.<br />
The lift force is present only if airflow past the object is unsymmetrical (i.e. faster above or below the<br />
object). This asymmetry can result from the shape <strong>of</strong> the object itself (this effect is exploited in the