Physics III: Fluids and Thermodynamics

Question 1

As an ideal fluid flowing in a narrow pipe passes from a region of cross-sectional diameter d to a region of cross-sectional diameter d / 2, the flow speed of the fluid will:

A. decrease by a factor of 4.

B. decrease by a factor of 2.

C. increase by a factor of 2.

D. increase by a factor of 4.

Answer 1

D. increase by a factor of 4.

If the diameter of the flow tube decreases by a factor of 2, the cross-sectional area decreases by a factor of 2² = 4. Since the Continuity Equation implies that flow speed is inversely proportional to the cross-sectional area of the flow tube, so the flow speed will increase by a factor of 4.

Question 2

vasoconstriction increases/decreases blood flow?

Answer 2

decreases

Question 3

Elastic properties relate to the tendency of a material to maintain its shape and not deform when a force is applied to it. A material such as steel will experience a smaller deformation than rubber when a force is applied to the materials and is therefore said to have higher elastic properties because their rigidity makes them act like springs that control how quickly its particles return to their original positions. Steel is a rigid/elastic material while rubber deforms easily and is a more flexible/less elastic material.

Answer 3

Therefore, sound can travel faster through mediums with higher elastic properties (like steel) than it can through solids like rubber, which have lower elastic properties.

Question 4

P_gauge = ρgh

Answer 4

equation for hydrostatic pressure in units of Pa _{(Pa is N/m^{<span>2</span>})}

P=pressure of gauge (ie the pressure of the system due to water above object regardless of external pressure such as surface gas pressure and atmosphere)

ρ = density_fluid (mass/volume in kg/m³)

g= acceleration d/t gravity = 10 N/kg

^{(instead of m/s2 because it’s in fluid)}

h=height between object and top of fluid (ie depth)

^essentially you are determining the pressure due to the water mass of water above the object

Question 5

T/F: density of a liquid remains constant

Answer 5

true.

This means that the hydrostatic gauge pressure will increase proportionally with both density and depth

Question 6

Difference between hydrostatic gauge pressure an total hydrostatic pressure?

Answer 6

hydrostatic gauge pressure: only expresses the pressure within the system and is proportional to depth

total hydrostatic pressure is P_atm + P_gauge and is not proportional to depth.

Question 7

what variations can you have in a gas system that affects thermodynamics

Answer 7

Question 8

what is the value of density of water

Answer 8

1000kg/m³

or, 1g/cm³

Question 9

what is the unit of pressure for fluids

Answer 9

the pascal, Pa= 1N/m²

e.g. sea level: 1 atm= 100kPa (kilopascals)

Question 10

T/F: hydrostatic gauge pressure does not depend on area of fluid in the system

Answer 10

true.

only depth matters (ie height from surface)

calculation would be the same whether youre in swimming pool or in an ocean

Question 11

_________rather than net force determines whether a body moves or remains at rest in a fluid

Answer 11

pressure difference

Question 12

equation for density

Answer 12

ρ=m/v

Question 13

how do you determine specific gravity?

Answer 13

sp. gr. = ρ/ρ_H2O

where ρ_H2O is 1000kg/m³

since the units kg/m³ cancel out, sp. grav. is unitless

you can also use specific gravity to find density of a substance by rearranging the equation

*a substance with a density that is n times the density of water will have a specific gravity equal to n

Question 14

bouyant force is defined as

Answer 14

the net force exerted on an object that is partially or fully submerged due to the pressure difference between the area of water above vs area of water below the object

Question 15

what is the magnitude of the bouyant force?

Answer 15

equal to the weight of the fluid displaced by the object (Archimedes principle)

this translates to the equation: F_Bouy=ρ_fluidV_subg

(from F=ma)

ρ_fluidV_sub = mass of displaced fluid

V_sub =volume of the portion of the object that is submerged, also equal to the volume of displaced fluid

Question 16

T/F: the pressure on a submerged object is greater pushing up than pushing down on the object

Answer 16

true

and the pressure increases with depth of submersion, from P_gauge​=ρgh

this is simply due to the fact that the pressure is greater at the location in the fluid that corresponds with bottom of object

Question 17

hydraulic jack scenario

Answer 17

two pistons rest above two cylinders of different cross-sectional areas, connected by a pipe/passageway.

Pascal’s law: the force exerted on the smaller cylinder equals the force exerted upwards on the other cross-sectional area.

Question 18

what is the relationship between force and area in a hydraulic jack

Answer 18

the pressure increase on the body of fluid is

F₁ / A₁

by Pascal’s law, F₁ / A₁=F₂ / A₂

⇒ F₂ inversely proportional to A₁

Question 19

what is the relationship of distance and area for a hydraulic jack?

Answer 19

A₁d₁ =A₂d₂

_⇒ d₂ inversely proportional to A₂

_{<span>where distance is the amount an object on the surface is pushed up as a result of the force applied to fluid on opposite side.</span>}

Question 20

specific gravity

Answer 20

ration of density of an object to density of water (can be a trick way of comparing density)

specific gravity is directly proportional to density

Question 21

for a floating object, the fraction of it that is submerged is the same as the fraction/ratio of

Answer 21

its density to the fluid’s density

expressed as: V_sub/V= ρ_object /ρ_fluid

_{*recall that} ρ_object /ρ_{fluid <em>is</em> specific gravity}

Question 22

what occurs when an object happens to have the same density as the fluid in which it exists?

Answer 22

it will hover in static equilibrium just underneath the fluid

Question 23

flow speed is directly/indirectly proportional to the r² of the cross-section (cross-sectional area)

Answer 23

indirectly

equation is: A₁V₁ =A₂V₂

Question 24

what is 0.5²

Answer 24

NOT 2.5… imagine it in fraction form before trying to calculate it to get better number sense then use decimal moving trick to calculate it

The answer is 0.25

Question 25

what are the conditions for an ideal fluid?

Answer 25

1. fluid is incompressible ρ constant
2. there is negligible viscosity (friction/cohesion of molecules within fluid molecules) _{<em>blood would violate this condition</em>}
3. flow is laminar (opposite of turbulent)
4. flow rate is steady (volume of fluid constant)

*If these conditions apply, then there is conservation of total mechanical energy of the fluid (Bernoulli’s Equation)

Question 26

“density is the _____ of fluid”

Answer 26

mass

^the application for this is that in the Bernoulli and other equations, there are expressions that match KE and PE except with m replaced by ρ

Question 27

Bernoulli’s Equation

Answer 27

only applies to fluids that follow the conditions of an ideal fluid

y=height with respect to horizontal reference point (usually the lowest point of the system. If the point of reference is not given it can be assumed to be zero for ease of calculation. then “y₁” is zero and ρgy₁ is removed from the equation)

also, watch out for when P is atm pressure

also when the question asks for the gauge pressure you’re just finding P-P_atm

Question 28

What’s the Bernoulli effect?

Answer 28

it describes the phenomenon that pressure is lower where the flow speed is greater. (in reference to fluids or air where y (height from reference point is equal)

and by extension:

↑area↓flow speed↑pressure

(this comes from the idea that pressure is greater in areas of greater volume (a similar thing happens with pressure increasing with depth)

*This ONLY applies to a situation where flow rate is the same (does not apply to vasodilation/vasoconstriction)

Question 29

As blood travels the arteries into the capillaries the total cross-sectional area increases/decreases, which means the velocity increases/decreases

Answer 29

As blood travels the arteries into the capillaries the total cross-sectional area increases which means the velocity decreases

*because you are added up all the individual cross-sectional areas of each capillary tube

Question 30

how do you determine the amount of a submerged object that is above or below the surface of a fluid

Answer 30

V_sub/V_fluid=ρ_sub/ρ_fluid

this fraction gives you the percent of object submerged

*watch out for when a question is actually asking about volume above

Question 31

What do you do with a specific gravity number?

Answer 31

find the density of the object with that specific gravity by using equation sp. gr. = ρ/ρ_H²0

ρ_{H²0 = 1000kg/m³}

solving for density, we get (sp. gr.) x (1000kg/m³)

Question 32

how do you find an object’s weight in water?

Answer 32

w_object = ρ_object V_object g

similar to finding bouyant force (F_Bouy=ρ_fluidV_subg) but with respect to the object instead of the fluid

^this equation get’s you the true weight

to find the apparent weight calculate:

w_apparent=w_object –F_Bouy

Question 33

flow rate is

Answer 33

the volume of fluid that passes a given point per unit time in m³/s

Q = Av

Q=flow rate

A= area of pipe at the given point

v= average velocity at given point

Question 34

continuity equation states that:

Answer 34

Q₁=Q₂

so, A₁v₁ =A₂v₂

Question 35

stress on a solid object is measured by

Answer 35

P_stress = force/area

*unlike the equation for pressure used in other scenarios, the force in thie equation does not need to be perpendicular to the object

stress on a solid object can be:

1. squeeze/compression
2. stretch/tension
3. bend/shear

Question 36

stress on an object is directly/inversely proportional to the cross-sectional area to which the force is applied

Answer 36

inversely

where area of circular cross-section is radius or diameter* squared

*since radius and diameter are proportional you get the square of both, not just of the radius

Question 37

strain on a solid object undrgoing stress can be determined by

Answer 37

ratio of:

change : original length of object

if change is

1. tensile or compressive, then strain= ΔL/L_i
2. sheer strain (bending), then strain=D/L_i

_{D=displacement (see image)}

Question 38

Stress on an object measures_____.

Strain of an object measures ______

Answer 38

stress measures pressure. strain measures change

however, in actuality stress causes strain and Hooke’s law is what relates them together mathematically

Question 39

stress and strain are proportional when…

Answer 39

when the object has elasticity (meaning, it will go back into its original position once stress is removed)

This qualifies it as operating under Hooke’s law (law of springs)

Question 40

Hooke’s Law

Answer 40

stress = modulus x strain

modules is a constant

*stress is the only expression with units so when solving for the other variables, use the units of stress (Pa)

Question 41

what is the equation for shear force

Answer 41

X=FL_i/AG

_{from F/A=GX/Li ​hooke’s law}

_{mnemonic: you wave a FLAG from shear joy}

Question 42

what is the equation for tensile or compressive force

Answer 42

ΔL=FL_i/EA

from F/A=GX/L_i ​hooke’s law

_{mnemonic: you would FLEA from a tense or compressive situation}

Question 43

Hooke’s law states that

Answer 43

stress=modulus x strain

this has 2 literal applications:

1. springs: F_s= -kx
2. elasticity of solids: F/A=(EorY)(ΔL/L) →rearrange→ ΔL=FL/EA