Fluids and Solids Flashcards
density = ?
what are the SI units of density?
p=m/V
density=mass/volume
(kg/m3)
g/mL or g/cm3 also commonly used
what is the density of water in g/mL and kg/m3?
1 g/mL
1000 kg/m3
specific gravity = ?
specific gravity= densityobj/densitywater
(unitless)
- if an object’s specific gravity >1 it is more dense than water and will sink
- if an object’s specific gravity is <1 it is less dense than water and will float
- the specific gravity of an obj expressed as a percent tells you the percent of the obj’s volume that wil be submerged (ie. ice specific gravity=0.92 so 92% of it’s volume will be submerged in water)
pressure = ?
what are the SI units of pressure?
P=F/A
pressure=force/area
(Pascal = Pa= N/m2)
- scalar
- pressure cannot be negative
- force is perpendicular to area of contact
absolute pressure = ?
P=Po+pgh
where Po=pressure at the surface, which is typically 1 atm in most open air situations, but is not always the case ie. with pressure cookers
pgh=weight of fluid sitting above a submerged object at some height, h
absolute pressure= total pressure exerted on an object that is sumberged on a fluid (N/m2)
(note: fluids include liquids and gases)
guage pressure = ?
Pg=P-Patm
Pg= difference b/w absolute pressure inside and atm pressure outside ie. Pg=Psys-Patm
- Pg=(Po+pgh)-Patm so when Po=Patm, Pg=pgh at depth, h
- PB-PA=pg(depthB-depthA)
- height inverse to pressure
- NOTE: careful if using height or depth
what does a positive gauge pressure mean? negative?
positive gauge pressure means fluid will move out, negative gauge pressure means fluid will flow in
definition of pascal’s principle?
applied pressure is transmitted undeminished to all parts of the fluid and walls of the container (for incompressible fluids)
(ie why toothpaste tube works!)
- larger the area, larger the force, although larger force will be exerted through a smaller distance
pascals priniciple = ?
how would use density of a fluid to find the KE, U, and weight of the fluid?
archimedes’ principle definition?
an object wholly or partially submerged in a fluid will be buoyed up by a force equal to the weight of the fluid that it displaces
- obj submerged will cause a volume of fluid to be displaced equal to volume of obj submerged
- mass of fluid displaced exerts a force equal to its weight up against submerged obj=buoyant force
- therefore things will float when Fb=weight, rise when Fb> weight and sink when Fb < weight
buoyant force= ?
Fb=(Vfluid displaced)(pfluid)(g)
=(Vobj sumberged)(pfluid)(g)
Class Q: How how can water in a well travel up a pipe if you create a vacuum in the pipe?
A
floating
Fg=Fb
pobjVobjg=pfluidVsubmergedg
- can cancel gravity (gravity doesn’t matter!!) b/c mass object=mass fluid displaced (NOT equal volumes)
pobj/pfluid = Vsub/Vobj
- max this ratio could be is 1 b/c pobj < pfluid b/c obj is floating
C
because ice is less dense than water so when melts it shrinks into space below
ie. why when ice on land melts it will raise ocean levels but when ice already in the water melts, ocean levels remain the same)
sinking
Fnet=Fg-Fb
apparent weight=true weight-“lost”weight
- Fg=pobjVobjg and Fb=pfluidVsubg so since the volumes are the same because its sinking only difference is the densities!
Fg/Fb = pobj/pfluid
surface tension def
surface tension causes liquid to form “thin strong layer of skin” at surface that results from choesion
cohesion def
attractive force b/w like molecules
(causes surface tension)
adhesion def
attractive force b/w a molecule of liquid and a molecule of some other substance
(causes meniscus upward when adhesive forces > cohesive an “upside down” mmeniscus when cohesive forces > adhesive forces)
mercury is the only metal at room temp that has an upside down meniscus
viscosity def
resistance of a fluid to flow
(honey= very viscous)
- low viscousity fluids behave like ideal fluids
- more viscous fluids lose more energy to friction
- SI unit is N*s/m2
what is the difference b/w laminar and turbulent flow?
- laminar flow=smooth and orderly as layers of fluid flow parallel to each other (layers closest to wall of a pipe flow more slowly than those at the center though)
- turbulent flow=rough and disorderly- arises when velocity of fluid exceeds critical velocity, vc. Leaves eddies behind obstacles
- MCAT always assumes laminar flow
critical velocity = ?
vc=(Nrµ)/pD
Nr=reynold’s number
µ=viscocity
p=density of fluid
D=diameter of pipe
continuity equation = ?
A1v1=A2v2
- fluids will flow more quickly through narrower passages and more slowly through widers ones (ie. when go from artery to capilaries area increases so velocity decreases)
- Av=Q=constant volume flow rate (m3/s)
cardiac output = ?
- CO (L/min)= blood pressure/vascular resistance
- CO= heart rate (beats/min) * stroke volume (L/beat)
Cardiac Output=Volume Flow Rate
type VR for 20 y/o is 5-6L/min
- Bernoulli’s eqtn is absolute pressure + dynamic pressure (pressure associated w/ mvmnt of fluid like KE) + guage pressure (like PE)
- since P + pgh = static/absolute pressure then bernoulli’s eqtn simply conservation of energy eqtn where the sum of static pressure and dynamic pressure will be constant in a closer container
- therefore, if more energy is dedicated towards fluid mvmnt that means less energy will be dedicated towards fluid pressure
- can only use for ideal fluids (i.e. with no viscocity aka why can’t use for blood flow b/c of vascular resistance, except over very short distances)
application: explain how bernoulli’s eqtn relates to plane lift
- propellers and jet engines generate thrust by pushing air backward
- the top of a wing is curved and the bottom is flat, so air must move faster over the top of the wing and slower underneath it. A slower velocity under the wing means more energy can be put into force, therefore the slower air exerts more force on the plane than the faster air, causing plane to lift
as seen in MCAT, typically will be given question where fluid moving through series of horizontal pipes so avg height of fluid is constant… what happens to the eqtn?
the pgh on both sides of the eqtn cancel out leading to inverse relationship b/w static and dynamic pressure
as velocity of fluid increases, static pressure decreases
what are the three relationships from bernoulli’s eqtn?
1- need to remember
2- hydrostatic pressure eqtn
3- kinematics, P1=P2 means no work done (b/c W=PV)
Explain how it relates to a tornado passing through and which way windows will burst
tornado outside= high speed air (fluid) so low pressure, therefore higher pressure inside and fluild wants to go from high –> low pressure so windows will burst out
Class Q: One of the manifestations of atheroscleriosis is narrowing of the arteries. Relative to a section of healthy artery, what can you predict about the pressure exerted on the walls of a narrowed artery?
cardiac output:
Q= (P1-P2)/R
Q= volume flow rate (cardiac output)
P1-P2=pressure diff. created by heart (blood pressure)
R=total vascular resistance to flow
all of these are equiv to what in an EMF circuit?
3 things to know:
- resistance is inversly proportional to what?
- volume flow rate is proportional to what?
- what is the dominant contributor to flow resistance?
- resistance inversely proportional to r4 (radius of vessle)
- therefore volume flow rate is proportional to r4
- small vessles (arterioles) are dominant contributors to flow resistance
therefore heart will get bigger to try and generate amount of pressure needed to increase flow rate as arterioles get blocked so proper amnt of blood can be pumped out
what is normal systolic BP?
normal diastolic BP?
systolic: 110-120
diastolic: 70-80
Young’s modulus = ?
Y= (F/A) / (∆L/L) = stress/strain
- F is perpendicular to surface
- from a stretching (tensile) or pushing (compression force)
- applied pressure= stress
- change in length per unit length= strain
- Y constant for a given solid material
- Y in (Pa)
Shear modulus = ?
S= (F/A) / (x/h) = stress/strain
- if force applied parallel to obect’s surface shearing shift in direction of force
- x= lateral movement in direction of force (x)
- h=height of object (y)
- same stress as Young’s modulus but diff strain
Bulk modulus = ?
B= (F/A) / (∆V/V) = stress/strain
- way a solid will experience a change in volume from applied pressure
how does the bulk modulus of a material relate to the speed of sound through that material?
does sound travel faster in solids, liquids or gases?
vsound proportional to √B
therefore, sound travels fastest through solids, then liquids then gases
do solids/liquids or gases have a higher B?
- solids/liquids have a greater B b/c larger amounts of pressure must be applied to effect a ∆V whereas gases easily compressible= small B
Class Q: what would have a greater Young’s modulus steel or silly putty?
Steel. (smaller strain–> bigger Y)
- graph, see that linear relationship stress/strain is slope=Y (steel will have a greater slope)
- blue dots=at same pressure, silly putty has more strain
- if apply so much stress to system, can permanently deform object (=yield strength/elastic limit) then relationship no longer linear. When object breaks=ultimate strength
thermal expansion = ?
∆L= aLo∆T
where a=coeff. of thermal expansion
things expand when temp rises and contract when temp falls, so when see ∆L think either Young’s modulus or thermal expansion
(also volume expansion: ΔV = βVoΔT and area expansion: ΔA = γAoΔT)
