fluids Flashcards
density
p=m/V, scalar quantity
p(rho) is density, m is mass, and V is volume; units: Kg/m^3 or g/mL = g/cm^3
density of water
1 g/cm^3= 1000 kg/m^3
weight of volume of a fluid
F=pVg
seen often with buoyancy problems
specific gravity
SG= p/ 1 (g/cm^3), unit less
good for determining if something will sink or float in water
Pressure
a ratio of the force per unit area; scalar quantity
P= normal force vector (F)/ area (A)
unit: 1 pascal (Pa)= 1 N/m^2
other units for pressure
1.013 x 10^5 Pa = 760 mmHg = 760 torr =1 atm
Absolute pressure
sum of all pressures at a certain point within a fluid; it is equal to the pressure at the surface of the fluid plus the pressure due to the fluid itself
absolute hydrostatic pressure
pressure on an object submerged in a fluid
P (absolute pressure)= incident or ambient pressure, the pressure at the surface (Po) + pgz
(z=depth of the object)
in open air, Po is 1 atm
gauge pressure
the difference between absolute pressure and atmospheric pressure. in liquids, gauge pressure is caused by the weight of the liquid above the point in measurement
P gauge= P-Patm= (Po+pgz)-Patm
hydrostatics
the study of fluids at rest and the forces and pressures associated with standing fluids
Pascal’s principle
states that a pressure applied to an incompressible fluid will be distributed undiminished throughout the entire volume of the fluid
P (pressure)= F1/A1=F2/A2
V (volume)= A1d1=A2d2
work as a product of constant pressure and volume change
it is an isobaric process
W=PxdeltaV= F1d1=F2d2
Archimede’s principle
governs the buoyant force. when an object is placed in a fluid, the fluid generates a buoyant force against the object that is equal to the weight of the fluid displaced by the object
buoyant force
Fbuoy=p(fluid)V(fluid displaced)g=p(fluid)V(submerged)g
what will happen when an object is more dense then the fluid that it is in?
the object will be completely submerged because the volume of displaced fluid will not exert a buoyant force equal to the weight of the object, so the object will sink to the bottom
what happens to an object that is placed in a fluid that’s density is greater then the object?
it will sink into the fluid only to the point at which the volume of displaced fluid exerts a force that is equal to the weight of the object
cohesion
the attractive force that a molecule of liquid feels toward other molecules of the same liquid; gives rise to surface tension (liquid that forms a thin but strong layer)
adhesion
the attractive force that a molecule of the liquid feels toward the molecules of some other substance
meniscus
curved surface in which the liquid “crawls” up the side of a container; happens when the adhesive forces are greater then the cohesive forces
fluid dynamics
the study of fluids in motion
viscosity (eta)
the resistance of a fluid to flow, increase to this increases the viscous drag; should be ignored on questions unless other wise stated
units: (Pa)(s)=(Nxs)/m^2
viscous drag
a nonconservative force that is analogous to air resistance. objects moving through the liquid will experience this viscous drag
ideal fluids
have no viscosity and are described as inviscid
what happens to liquids with higher viscosity in regards to energy?
they lose more energy then liquids with lower viscosity`
laminar flow
smooth and orderly, and is often modeled as layers of fluid that flow parallel to each other, however the layers will not necessarily have the same linear speed
poiseuille’s law
used with laminar flow through a pipe or confined space
Q= (pi r^4 deltaP)/ (8 eta L)
Q=flow rate r= radius of the tube deltaP= pressure gradient eta=viscosity of the fluid L=length of the pipe
turbulent flow
rough and disorderly. turbulence causes the formation of eddies; lose lots of energy due to frictional forces
eddies
swirls of fluid of varying sizes occurring typically on the downstream side of an obstacle, occurs when the speed of the fluid exceeds the critical speed
critical speed
depends on the physical properties of the fluid, such as viscosity and the diameter of the tube
vc= (Nr x eta)/ (pD)
D=diameter vc=critical speed Nr=dimensionless constant (Reynolds number) eta= viscosity of the fluid p=density of the fluid
streamlines
indicate the pathways followed by tiny fluid elements
linear speed
a measure of the linear displacement of fluid particles in a given amount of time
continuity equation
Q= v1A1=v2A2
v=linear speeds of the fluid at point 1 and 2
A=areas at point 1 and 2
Q=flow rate
Bernoulli’s Equation
an expression of conservation of energy for a flowing fluid; states that the static pressure and dynamic pressure will be constant between any two points in a closed system
P1+(1/2pv1^2)+pgh1=P2+(1/2pv2^2)+pgh2
P=absolute pressure of the fluid p=density v=linear speed g=acceleration due to gravity h=height of the fluid above some datum
dynamic pressure
1/2pv^2
static pressure
P+pgh
what generates more pressure, faster or slower moving fluids?
slower moving fluids will exert more static pressure
Venturi effect
for a horizontal flow, there is an inverse relationship between pressure and speed, and in a closed system, there is a direct relationship between cross sectional area and pressure exerted on the walls of the tube
