Fluids and Solids

Question 1

density = ?

what are the SI units of density?

Answer 1

p=m/V

density=mass/volume

(kg/m³)

g/mL or g/cm³ also commonly used

Question 2

what is the density of water in g/mL and kg/m³?

Answer 2

1 g/mL

1000 kg/m³

Question 3

specific gravity = ?

Answer 3

specific gravity= density_obj/density_water

(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)

Question 4

pressure = ?

what are the SI units of pressure?

Answer 4

P=F/A

pressure=force/area

(Pascal = Pa= N/m²)

• scalar
• pressure cannot be negative
• force is perpendicular to area of contact

Question 5

absolute pressure = ?

Answer 5

P=P_o+pgh

where P_o=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)

Question 6

guage pressure = ?

Answer 6

P_g=P-P_atm

P_g= difference b/w absolute pressure inside and atm pressure outside ie. P_g=P_sys-P_atm

• P_g=(P_o+pgh)-P_atm so when P_o=P_atm, P_g=pgh at depth, h
• P_B-P_A=pg(depth_B-depth_A)
• height inverse to pressure
• NOTE: careful if using height or depth

Question 7

what does a positive gauge pressure mean? negative?

Answer 7

positive gauge pressure means fluid will move out, negative gauge pressure means fluid will flow in

Question 8

definition of pascal’s principle?

Answer 8

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

Question 9

pascals priniciple = ?

Answer 9

Question 10

how would use density of a fluid to find the KE, U, and weight of the fluid?

Answer 10

Question 11

archimedes’ principle definition?

Answer 11

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 F_b=weight, rise when F_b> weight and sink when F_b < weight

Question 12

buoyant force= ?

Answer 12

F_b=(V_{fluid displaced})(p_fluid)(g)

=(V_{obj sumberged})(p_fluid)(g)

Question 13

Class Q: How how can water in a well travel up a pipe if you create a vacuum in the pipe?

Answer 13

Question 14

Answer 14

A

Question 15

floating

Answer 15

F_g=F_b

p_objV_objg=p_fluidV_submergedg

• can cancel gravity (gravity doesn’t matter!!) b/c mass object=mass fluid displaced (NOT equal volumes)

p_obj/p_fluid = V_sub/V_obj

• max this ratio could be is 1 b/c p_obj < p_fluid b/c obj is floating

Question 16

Answer 16

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)

Question 17

sinking

Answer 17

F_net=F_g-F_b

apparent weight=true weight-“lost”weight

• F_g=p_objV_objg and F_b=p_fluidV_subg so since the volumes are the same because its sinking only difference is the densities!

F_g/F_b = p_obj/p_fluid

Question 18

surface tension def

Answer 18

surface tension causes liquid to form “thin strong layer of skin” at surface that results from choesion

Question 19

cohesion def

Answer 19

attractive force b/w like molecules

(causes surface tension)

Question 20

adhesion def

Answer 20

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

Question 21

viscosity def

Answer 21

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

Question 22

what is the difference b/w laminar and turbulent flow?

Answer 22

• 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, v_c. Leaves eddies behind obstacles
• MCAT always assumes laminar flow

Question 23

critical velocity = ?

Answer 23

v_c=(N_rµ)/pD

N_r=reynold’s number

µ=viscocity

p=density of fluid

D=diameter of pipe

Question 24

continuity equation = ?

Answer 24

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)

Question 25

cardiac output = ?

Answer 25

• 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

Question 26

Answer 26

• 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)

Question 27

application: explain how bernoulli’s eqtn relates to plane lift

Answer 27

• 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

Question 28

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?

Answer 28

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

Question 29

what are the three relationships from bernoulli’s eqtn?

Answer 29

1- need to remember

2- hydrostatic pressure eqtn

3- kinematics, P₁=P₂ means no work done (b/c W=PV)

Question 30

Explain how it relates to a tornado passing through and which way windows will burst

Answer 30

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

Question 31

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?

Answer 31

Question 32

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?

Answer 32

Question 33

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?

Answer 33

• 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

Question 34

Answer 34

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

Question 35

what is normal systolic BP?

normal diastolic BP?

Answer 35

systolic: 110-120
diastolic: 70-80

Question 36

Young’s modulus = ?

Answer 36

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)

Question 37

Shear modulus = ?

Answer 37

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

Question 38

Bulk modulus = ?

Answer 38

B= (F/A) / (∆V/V) = stress/strain

• way a solid will experience a change in volume from applied pressure

Question 39

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?

Answer 39

v_sound proportional to √B

therefore, sound travels fastest through solids, then liquids then gases

Question 40

do solids/liquids or gases have a higher B?

Answer 40

• 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

Question 41

Class Q: what would have a greater Young’s modulus steel or silly putty?

Answer 41

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

Question 42

thermal expansion = ?

Answer 42

∆L= aL_o∆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 = βV_oΔT and area expansion: ΔA = γA_oΔT)