Fluids Chp. 10AP Physics Groff 2013

Pressure

A fluid is a Liquid or a gas, it can flow and fill the shape of any container.

Pressure is defined as the ratio of a force applied to a specific area.

P=F/A P=Pressure…measured in Pascal..Pa F=Force…measured in Newtons..N A is Area…Measured in m^s

Pressure Cont.

Hydrostatic Pressure The pressure applied by the weight

of a fluid. Think of a column, A column of fluid applies pressure due to the weight of the fluid above it.

Calculating Pressure

Since P=F/A where F is the weight =mg

P= mg/A

Mass is not commonly used to measure fluids, Volume is most commonly used. The relationship between mass and volume is Density. ρ=m/v ρ=Density…kg/m^3 M=mass…kg V is volume…m^3

Calculating Pressure cont…

Therefore the mass of a fluid can be described in terms of the density and the volume of the fluid.

M=ρV

Substituting this for m in the pressure equation P=ρVg/A

The volume of the column is the Area of the base of the column multiplied by the height of the column.

V=Ah

Calculating pressure cont.

Substituting this expression in for the volume P=ρAhg/AThis can be simplified to P=ρgh

Height of column measured in …meters m

Gauge Pressure and it’s Calculation

The pressure due to just the column of fluid is often referred to as the gauge pressure. Gauge pressure is the difference in the pressure applied to the top of the column of fluid,(the atmospheric pressure), and the absolute pressure, the total pressure at the bottom of the column.

Pgauge =P absolute –P atmos/applied

(Pgauge= P-P0 )

Pgauge=ρgh

P=Po+ Pgauge

Pgauge is gauge pressure

P is the absolute pressure

Po is the atmospheric pressure, 1.01 x 10^5 Pa @ sea level. (101KPa)

Buoyancy When an object is placed in a fluid, the object will float or sink. In both

cases fluid is displaced.

Archimedes principle states: the weight of the fluid displaced is equal to the upward force exerted on the object by the fluid. This is called the buoyant force.

Fbuoy= mf g;

Most fluids are not measured in terms of mass, but in terms of Volume, so: M=ρv Then buoyant force is

Fbuoy=ρfvfg

Force…Newtons ρ…density Vf…is the volume of the fluid displaced

Buoyancy Cont…

When an object sinks, the buoyant force is less than the weight of the object. The volume of the fluid displaced is equal to the volume of the object. Since the forces are unbalanced, the object will accelerate downwards (until it reaches terminal velocity)drag cannot be ignored!

Common Situations Involving Buoyant ForceObject

Situation FBD Force Equations

Floating, partially submerged

Fbuoy

Fg

ΣF=ρfVfg – mg=0

Cont..

Object floating, completely submerged (max weight of the object for floating)

Fbuoy

Fg

ΣF=ρfVfg – mg=0

Vfluid =Vobject

Cont.. F buoy

Fg

ΣF=ρfVfg – mg=ma

Object Sinking…Jack “don’t let go” Rose “I’ll never let go Jack”-Rose lied.

Cont.

Fspring Fbuoy

Fgrav

Object suspended in a fluid, attached to a spring.