Fluid Mechanics
the study of forces that fluids (air, water) exert on objects moving through them
- includes: buoyant and dynamic forces
buoyant force
due to immersion in fluid
-tendency to be lifted up
dynamic force
due to relative movement in fluid
- lift force
- drag force
An object submersed in water will experience…
- pressure from the weight of the water above
- pressure from the water beside
- pressure from the water below to hold up the object and the water above the object
- submerging the object deeper in the water the force (pressure) above and below increase
Pressure on submerged objects in water
- the force below the object will always be higher than the force above it
R(lower) - R(upper) = buoyant force
-the difference between the force above and the force below is related to the weight of the volume of fluid displaced, therefore the buoyant force will always be acting up because more will have been displaced at the bottom than at the top
determining if an object will float
R(lower) - R(upper) = buoyant force
Weight of object (W = mg)
- buoyant force = mg, object will be in static equilibrium
- buoyant force > mg, object will accelerate upwards
- buoyant force < mg, object will accelerate downwards
Floating/ sinking due to density
density = mass / volume
P = m/v
if something is more dense than water it will sink and vice versa
- muscle/bone are more dense than water (will sink)
fat is less dense (will float)
Point of application? can’t think of a better word
- force due to gravity and buoyant forces do not always act through the same point
- Fg acts through CofG (related to body orientation and distribution of mass, density of tissues), Fb acts through centre of volume
Air and Buoyant forces
yes, air exerts a buoyant force but because our densities are so different we don’t notice it
Dynamic fluid force
is proportional to:
- density of the fluid
- surface area of the object immersed in the fluid
- relative velocity of the object to the fluid (squared)
- relative velocity is the difference between the objects velocity and the fluids velocity and is the most important factor in determining dynamic fluid force
Drag Force
a component of dynamic fluid force that opposes (parallel but opposite direction) the relative motion of the object with respect to the fluid
Types of Drag force
Surface drag
- the sum of the friction forces acting between the fluid molecules and the surface of the object
Form drag
- a result of how fluid molecules travel around an object due to the objects shape
Surface drag
also called skin friction or viscous drag
- as a molecule slides past the surface of an object, the friction between the surface of the object and the molecules in the fluid creates a layer of molecules called a boundary layer (laminar layer)
- the surface drag is due to the boundary layer of molecules that come in contact with the object and “rub up against” it
Surface drag in sports (swimming)
swimmers shave their body to reduce drag and they wear swim caps and special types of suits to reduce drag on their bodies in the water
Surface drag is affected by…
1) coefficient of drag (similar to friction)
- coefficient of drag is affected by the roughness of the surface and viscosity of the fluid
- shaving, bodysuits
2) density of the fluid
3) cross sectional area of the object
4) relative velocity (squared)
- how quickly the object and the surface are moving
Form Drag
- fluid traveling around any fairly smooth object will travel in a path called laminar flow
- laminar flow is when the fluid molecules diverge at the point of contact of the object and then converge after the object has passed (a wake)
- the amount of divergence depends on the shape of the object and the convergence is a result of the natural flow of fluid to rebalance pressure
- rebalance because the laminar flow causes a vacuum behind the object and a high pressure area at the point of contact that opposses forward motion
the shape of an object can influence the form drag on it…
- it minimizes the change in direction of the molecules first contact with the object
- takes up space where the turbulent flow or vacuum would occur behind the object
- football shaped object does the best
Form drag is affected by…
1) shape of the object
2) drag coefficient
3) density of the fluid
4) cross sectional area of the object
5) relative velocity (squared)
Drag and sport
- make body or clothing smoother
- streamline the shape of the body or equipment
- i.e. track cycling helmets are designed to nullify the vacuum created behind the athlete
- tailgating
- body position
Golf and Drag
the dimples on a golf ball create tiny pockets of turbulence which then pull the ball along and keep the air passing by closer to it, thereby minimizing the turbulent wake behind it by changing the laminar flow
Lift force
- is the dynamic fluid force component that acts perpendicular to the relative motion of the object with respect to the fluid
- used to change the direction of the relative motion of the object through the fluid
- determined by the direction of flow of the fluid
Lift force is caused by…
- lateral deflection of fluid molecules as they pass the object
- object exerts lateral force on molecules as molecules exert an equal but opposite lateral force on the object causing lift
- Lift is proportional to the lateral acceleration of the fluid molecules amd the mass of the molecules that are deflected
- the shape and orientation of the object can modify the effect of the lift force
Spoilers and lift force
the spoilers on cars actually push it down so that the tires can grip the road better
Spin and the Magnus effect
- the magnus effect explains the flights of spinning balls in sports
- it can be described using Bernoulli’s principle
- faster moving fluids exert less pressure than do slower moving fluids
- if a ball is spinning in the same direction as the fluid there will be a decrease in pressure
- If a ball is spinning in the opposite direction as the fluid there will be an increase in pressure
