EK Physics Ch3 Fluids

Question 1

density

Answer 1

p= mass/ volume

so it is defined as how much mass the fluid contains in a specifid volume V

SI units are kg/m³

unless otherwise stated, assume that all liquids and solids are totally incompressible adn for this reason have constant density, in reality gases are much mroe ocmpressible than liquids and liquids are far more compressible than solids.

-gases change volume and therefore density as ideal gas law describes, PV=nRT

Question 2

density formula

Answer 2

=how much mass per volume

= p (row) = mass/volume so density is kg per meter 3

Question 3

specific gravity

Answer 3

SG = psubstace/p water

a specific gravity of a substance is the density of that substance divided by density of water

-less than one indciates a substace lighter than water, one indicates a substance equally as heavy was water, greater than one indicates a substance heavier than water

Question 4

density of water

Answer 4

p= 1000 Kg/m³

p= 1 g/cm^3

Question 5

fluid pressure

Answer 5

p= F (force)/ A (area)

Question 6

fluid pressure

Answer 6

pressure experienced by object as a result of the impulse of molecular collisions

• it is the average of the magnitudes of the change in momentum of these collisions divided by the time duration of the collisions and the area over which these collisions occur

si unit = pascal, Pa

PRESSURE IS SCALAR, it has no direction!

• it exists in a fluid whether or not an object is immersed in that fluid
• its a type of stored energy per unit volume, units of pressure are equivalent to energy per unit volume, according to this definition, pressure is a measure of the energy due to the random velocities of molcules within a fluid distributed over the volume of the fluid

Question 7

pressure in kidneys

Answer 7

• kidneys are responsible for keeping blood pressure within a narrow range, to maintain this delicate balance, the kidneys modify glomerular filtration rate (GFR) through renin-angiotensin-aldosterone system RAAS
• released renin converts angiotensinogen to angiotensin I and angiotensin converting enzyme ACE converts angiotensin I to angeiotensin II
• angiotensin II signals the contraction of the efferent arterioles leading away from teh glomerulus
• when teh efferent arterioles contract, blood pressure in the glomerular capillary increases because resistance in these vessels is increased

Question 8

fluid at rest equation

Answer 8

p= pgy

p=density of the fluid

g= gravity 9.8

y= depth of the fluid or height

Question 9

fluid at rest

Answer 9

• experiences only forces perpendicular to its surface
• at any given depth hte pressure is equal to teh weight of hte fluid above a disk with area A divided by teh deare of the disk
• pressure is the same regardless of what area is chosen!

Question 10

total pressure at rest

Answer 10

ptotal= pgy1+p2gy2+p3gy3+p4gy4

additional fluids on top of the first fluid inc the total pressure by adding their weight, so sum the pressures

air is fluid so must add atm pressure if any fluid open to the atm, pressure can be found by p=pgy + patm

Question 11

atmospheric pressure

Answer 11

patm= 101,000 Pa

liquids boil when vapor pressure equals atm pressure** since atm pressure is inversely proportional to altiude, it is easier for a solution to boil at higher altitudes***

Question 12

pascal’s principle

Answer 12

• pressure applied anywhere to an enclosed incompressible fluid will be distributed equally/ undiminished throughout that fluid
• this is true becuase if pressure gradient exists btw two points with the same vertical distance from teh surface, fluid flows in the direction that relieves the differential
• since fluid pressure is a function of depth, the shape of the container does not affect it
• the pressure everywhere at a given depth in the same resting fluid will be constant

Question 13

ex air pressure

Answer 13

think of atm as a sea of air, as mov closer to the top and climb a mountain, your depth decreases

near the top there are fewer molecyules abov eyou, which means less weight and lower pressure

air pressure up here is low, making it tough to breathe

Question 14

gauge pressure

Answer 14

• refers to amount by which a system’s pressure deviates from atm
• P abs= p gauge + p atm
• pabsolute is hte pressure of a system relative to a vacuum
• pressure in chest for ex is lower than atm pressure
• the higher pressure of the atm pushes air into your lungs, same thing happens when suck straw, you create a partial vacuum inside the straw
• when you suck, vacuum doesnt really suck anything into it. The atm pressure pushes down on the fluid outside the straw pushing up the fluid inside the straw
• without atm pressure, a straw would not work!= remember in real life, physic never sucks

Question 15

gauge pressure 2

Answer 15

difference btw atm pressure and absolute pressure

Question 16

hydraulic lift

Answer 16

Question 17

hydraulic lift 2

Answer 17

• two pistons and a container enclose a standing incompressible fluid, a force on piston 1 applies a pressure on the fluid
• presure is transferred undimished to piston 2
• piston 2 has a greater area (look page 67) than piston 1, and force and area are directly proportional when pressure is constant, the force on piston 2 is proportionally greater than the force on piston 1, even though the presure is the same
• pressure applied on a fluid must be the same throughout
• a machine does not change work, if piston 2 moed the same distance as piston 1 while also experiencing greater force, the work done by piston 2 would be greater than the work done by piston 1
• instead hte force of piston 2 applied through a proportionally smaller distance, keeping work the same

Question 18

hydraulic lift 3

Answer 18

• notice that piston 1 has a much smaller area than does piston 2
• by pascal’s principle, both pistons must exert the same pressure at the point of contact with the liquid
• even if my pedal applies a relatively small force, its being applied to a simiarly small area
• the ratio of force to area will stay the same for piston 2, which with a larger area must be subject to a larger force

Question 19

force on fluids at rest

Answer 19

buyoant force

Question 20

buoyant force

Answer 20

​net force acting upwards = weight of water beign displaced is archimedes principle

net upward force due to fact more pressure on bototm then top is buoyant force! what makes things float!

• on any object is floarting or sunk in teh fluid
• pressure inc as a function of depth within a fluid at rest, p=pgy, so pressure is a measure of force per unit area, P= F/A
• so for a given cross sectional area A, an inc in pressure must be associated with an inc in force
• both pressure and force inc with depth, causing an object in teh fluid to experience both greater pressure and greater force at points farther from the fluid’s surface.
• As a result, the object experiences an upward force!
• upward force is called buoyant force becuase it has potential to buoy the object - to cause it to float

Question 21

Fb equation

Answer 21

Fb= p fluid X V fluid X g

Question 22

Fb analysis

Answer 22

• magnitude of the buoyant force experienced by an object, whether floating, submerged or sunk is directly proportional to the volume of the fluid it displaces, where p is density of fluid and V is volumeo ffluid displaced, g is acceleration due to gravity

Question 23

archimedes’ principle

Answer 23

• the upward buoyant force is equal in magnitude to the weight of the displaced fluid
• at depth along side of cube submerged in water, pressure will be the same on sides and offset each other; we know pressure is a functon of depth so pressure is greater on bottom of submerged cube, deeper into water, than presure on top of the cube
• F_N = Force acting upwards on this obejct, the pressure at bottom of object X surface area at the bottom of object (surface are for cube is d²) moinus pressure top times surface area on top
• so F_N= P(bottom)d² - P(top)d²
• Force = volume of water displased X density of liquid X gravity
• volume X density is mass of liquid displace, so net force is also equal to mass of liquid displaced X gravity**
• OR can say net force acting on this object= weight of liquid displaced**

Question 24

fraction of object submereged equation

Answer 24

V fluid/ V object

becuase pobject/ p fluid = m/v of object / m/v of fluid since m is same ends up with V fluid/ V object

Question 25

fraction of object submerged

Answer 25

• ratio of the density of floating object to the density of fluid in which it floats is equal to the fraction of the object submerged
• if object is floating in water, ratio equals the sepcific gravity of the floating object
• rememebr that the objec is floating on top of the fluid so the V of fluid is on the top!
• for floating object this ratio must always equal to or less than 1
• otherwise the fraction submerged would be greater than one, which is impossible!
• an object only floats when its density is less than the density of the fluid on which it floats
• exactly equal to its specific gravity!

Question 26

Pressure image

Answer 26

Question 27

terminology for gauge pressure and absolute pressure

Answer 27

Question 28

Pressure and depth

Answer 28

• remember pressure at point on bottom, pressure is acting in all directions including up, this makes sense because assuming static system, fluids stationary tells us the pressure in every direction must be equal! if you think about molecule of water if pressure down were greater than pressure up then object would start accelereating downard becuase surface area pointing upwards is the same as surface area pointing downwards, so even though pressure is function of how far we go pressure acting in every direction!

Question 29

pressure and depth 2

Answer 29

Question 30

Pascal’s law 2

Answer 30

Question 31

examples of 2 pressure gauges

Answer 31

Question 32

surface tension

Answer 32

• if drop needle on water it floats, should be more dense so sink its just sitting on surface because surface tension! water is a liquid capable of having significant amoutn of surface tension, know that because if push needle just below surface will sink like a stone to bottom of cup
• has this property because water molecules within this liquid are attracted to each other through H bonds with other water moelcuels aroudn this, pulled toward them called coehsion, so fact water and other liquid moelcules are attracted to eachother is called cohesion
• this has to do with surface tension btw water melcuels want to group together if they can, getting pulled also to left by other water molecules because component of that force that points in the direction of its original position as well as the one to hte left so it is restricted other water molecules in bulk of liquid have too many molecules pushing where it should be, at surface no wate rmoelcuels above it not as restricted so can group together form tighter better bonds, closer spacing form a tension not present in bulk of liquid; yes water moelcules down below prevnents them from formign oen big group in center, form tigther bonds at surface so can support a certain amoutn fo weight allowing needle to sit on top of liquid

Question 33

surface tension 2

Answer 33

Question 34

adhesion

Answer 34

water molecules attracted to wall, climb the wall a little bit

Question 35

cohesion

Answer 35

Question 36

adhesion v cohesion

Answer 36

Question 37

capillary action

Answer 37

• smaller tube greater affect of adhesion, water rises to high level within tube due to adhesions to walls of container when but small tube in bigger tube
• where fluid aided and transproted paritally by attraction to walls of container or tube it is flowing in**

Question 38

steady flow 1

Answer 38

Question 39

steady flow 2

Answer 39

Question 40

steady flow 3

Answer 40

Question 41

continuity equation

Answer 41

Question 42

Bernoulli’s equation 1

Answer 42

Question 43

Bernoulli’s equation 2

Answer 43

Question 44

Bernoulli 3

Answer 44

Bernoulli’s equation is essentially conservation of energy for fluids, and is given below:

P1 + ½ ρv12 + ρgh1 = P2 + ½ ρv22 + ρgh2

Here, the term that includes velocity (v) is analogous to the kinetic energy of the fluid, while the term that includes height (h) is analogous to the fluid’s potential energy. The remaining term is pressure (P). Importantly, this equation indicates that when height is constant (as in a horizontal pipe system), an increase in velocity corresponds to a decrease in pressure, and vice versa.

Question 45

airplane ex

Answer 45

Question 46

curve ball requires viscoisty

Answer 46

Question 47

Fluid statics units

Answer 47

Question 48

ex of p= F/A

Answer 48

Question 49

Principles about pressure

Answer 49

Question 50

Definitions of absolute and gauge pressure 2

Answer 50

Question 51

Barometer

Answer 51

Question 52

According to the passage, which of the following relationships must hold? (Note: 1 m3 = 1000 L.)

Answer 52

100 kPa is equivalent to 100 J/L.

This is a unit conversion problem:

100 kPa = 100,000 Pa = 100,000 N/m2 = 105 N/m2

100 J/L x (1000 L/m3) = 105 J/m3 = 105 Nm/m3 = 105 N/m2

Question 53

continuity equation

Answer 53

A final important relationship is given by the continuity equation (v1A1 = v2A2). This equation states that within a closed system, the flow rate of a liquid is constant, which indicates that the velocity of the fluid (v) is inversely proportional to the cross-sectional area that it is flowing through.

Question 54

viscosity

Answer 54

All liquids can flow, but some do so more easily than others. Resistance to flow—or more technically, resistance to deformation by shear stress—is known as viscosity.

A fluid that has a lot of friction with itself, won’t just natually move without resistance*

For the sake of the MCAT, viscosity can typically be considered negligible; additionally, fluids should be assumed to be incompressible, meaning that they have fixed volumes.***

Question 55

Poiseuille’s law

Answer 55

Poiseuille’s law is used to describe laminar flow of incompressible fluids through a long cylindrical tube.

Poiseuille’s law contains five variables: the flow rate (Q), the pressure drop between both ends of the tube (ΔP), the radius of the tube (r), the length of the tube (L), and the viscosity (η). It can be written in two equivalent forms, both of which are given below:

Question 56

laminar flow

Answer 56

The term laminar flow is used to describe scenarios in which a flowing fluid is composed of parallel layers that may be moving at different velocities. opposite of viscosity, glass, peanut butter, syrup all viscious vs perfect laminar flow*

In a nutshell, laminar flow corresponds to smooth, well-behaved flow that is easy to model. In contrast, in turbulent flow, the smoothly regulated layers of laminar flow break down.

Question 57

Fluids 1

Answer 57

• in general, a fluid takes the shape of container
• two ex. liquids and gases are fluids (both take shape of container)
• diff btw gas and liquid is that gas is compressible!! meaning can dec volume of container and gas just becomes denser, like air in balloon can squeeze ballon while liquid is not compressible ex. think of same balloon completely filled with water if squeezed on that balloon from every side you would not be able to change the volume of that ballon* no matter what you do or how much force or pressure put on it, versus if filled with gas can dec volume by inc pressure on all sides can squeeze it and makes it smaller

Question 58

Pascal’s principle 3

Answer 58

• any external pressure onto a liquid, an incompressible fluid, that pressure is distributed evenly thoughout the fluid shown using law of conservation of energy adn everythign we know about work= pascal principle
• any external pressure applied to fluid its distributed equally! extra compression will be distributd throughout the whole ballon or container, so inc pressure goes to the whole thing
• (part of fluids at rest!)

Question 59

pascals =

Answer 59

Newton per meter ²

Question 60

pressure at a depth in a fluid

Answer 60

• if tube of water, within cyldiner have a thin piece of foil or something that takes up the entire cross sectional area of this cylinder, want it to be an indicator of fluid if moving up or down or not
• since fluid completely static, nothing moving object will be static as well
• in order for something to be static/ not moving, know net force must be zero because no accerleration, velocity not moving constant, equals zero so net forces must be zero!
• force down= macceleration due to gravity, mg so Force down= mass of the fluid X gravitational constant*

if density = mass X volume, substitue mass = density X volume

SO p= pX h X g, downard pressure equals upper pressure because upward f is the same as downward force! b/c static lets us know upper force equal to downward force otherwise little cylinder sheet would move

if asked what weighs lb of feathers or lb of lead, they obviously way the same, key is volume cubic meter of lead weighs a lot more than cubic meter of feathers!!

Question 61

density of water ex

Answer 61

p= l000 kg/ m³

so if i go under water , pressur e= 1000 X 10 X 9.8= 9800 Pa is the pressure, near 1 atm pressure at sea level

using pressure = desnity X h X g

Question 62

specific gravity

Answer 62

how dense that substance is to water, specific gravity of mercurcy is 13.6

all that means is mercurcy is 13/6 X as dense as water! density of water is 1,000 kg/ m³

so densty of Hg= 13.6 X 1000 k kg/ m³

Question 63

specific gravity 2

Answer 63

density of that object/ density of water

density of water is 1000 kg / m³

gold 19,300/1000 = 19.3

ketchup = 1,400 so s.g. of ketchup is 1,400/1,000 = 1.4

For something that floats= specific gravity tells you fraction of that obejct that is submerged/ below water when floating!! ex. cube of wood with s.g. of 0.2 that means that 20% of total volume of wood will be submerged below water when floating, if cupe of wood had s.g. of 0.6 then 60% is submerged below water when floating

ice has s.g of 0.92 why 92% is actually underneath the water***

if cube is 2700 kg/m^3 s.g would be 270% but cant have more than 100% of object subegmed, max amoutn should be 100% so if s.g. of an object is >1 will sink if placed in water and have 100% of volume submerged***

Question 64

specific gravity 3

Answer 64

if let wood of density 638 kg/m^3 float in water with density of 850 can still find percent of wood submerged just use density of oil instead of density of water in specific gravity formula

638/850= 0.75 specific gravity so 0.75 < 1, so it floats with 75% of the wood’s volume submerged beneath the surface of the oil!

Question 65

There is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result?

Answer 65

When the cube is submerged, the object floats in equilibrium.

There must be a buoyant force keeping the object afloat pushing upward.

According to Newton’s Third Law, there should be an equal and opposite force downwards.

That additional force will cause the scale to register a weight greater than 80 pounds.

Question 66

When the gauge pressure is doubled, what happens to the absolute pressure?

Answer 66

Absolute pressure is equal to atmospheric pressure plus gauge pressure.

Atmospheric pressure is 101,300 Pa, while a typical gauge pressure for a tire is 30 psi or 207 Pa.

Since atmospheric pressure is relatively large compared to most gauge pressures, doubling the gauge pressure would not end up doubling the absolute pressure, but it would inc by a factor less than 2!

To use the tire example, if the gauge is 414 Pa, then absolute pressure would be 101,314 Pa. Absolute pressure increase by a factor less than 2.

Question 67

A patient is scheduled to receive an intravenous injection of medication that must be at least 109.3 kilopascals at the injection point before going into surgery. If the patient is lying on a bed 0.9 meters high, what is the minimum height above the ground that the nurse must suspend the bag to achieve that pressure at the injection point? pfluid = 1020 kg/m³

Answer 67

= 1.7 m

Question 68

on the moon, atmospheric pressure is ……

Answer 68

On the moon, there is less atmospheric pressure due to its much smaller mass and would be less than Po, specifically defined as atmospheric pressure on Earth. The y-intercept would start below P_oo​start subscript, o, end subscript.

Question 69

Which of the following scenarios most accurately represents Pascal’s law?

Answer 69

= the volume displacd by piston 1 is equal to the volume displaced by piston 2 in a hydrualic lift

Pascal’s Law states that pressure is transmitted undiminished to every portion of the fluid and to the walls of the container.

This allows us to write the equation P1= P2, and then F1/A1= F2/A2 as well as F1d1= F2d2.

As a result, we can explorate that a small force applied on a small area over a long distance will produce a large force applied on a large area over a short distance.

We also can deduce that W1/V1 = W2/V2. Since work is the same on both sides, the volume displaced by one side will be equal to the volume displaced on the other side in a hydraulic lift.

Question 71

Finding flow rate using bernoulli’s equation

Answer 71

Question 72

units of viscosity

Answer 72

Pa x s or 1 poise= 1/10 of a Pa Xs

or in other words 10Poise = 1 Pa X s

Fv= nAV/d

ex. viscosity of water at 0 degrees Celsius, not ice so not frozen yet is about 1.8 miliPascal seconds, so a centiPoise since 1 poise = 1/10 Pa X s

can see dependent on Temp, which we known when try to start car when freezing its harder; blood usually 3-4 cP

oil is around 200 cP

gases have viscosities even less, air has a viscosity of around 0.0018 cP (centi Poise)

if speed doenst depend on coefficient of viscosity then Newtonian fluid or if it doesnt depend ons peed then its nonNewtonian fluid

Question 73

poiseuille’s law equation

Answer 73

to know how much volume pass per a certain point per time:

volume / time= (delta p X pie X R^4)/ 8 X n(eta) X L

volme that will flow per time is depdendent on these, used to determine volume flow rate**

delta p= p1 - p2, pressure differential; if they are the same fluid wont flow very long has to be a difference, if want fluid to flow to right for instance p1 has to be greater than p2, greater the differnce more volume will flow per time

this R= radius of tube

eta= we know is the viscosity, so the viscosity of the fluid, which is inversely proportional to flow rate

more viscosity less it will flow, and more tube fluid has to flow through smaller flow rate*assume eta is not function of speed of fluid its Newtonian, and laminar flow means these layers of fluid stay in their lane they do not cross over, once get turbulence need much more complicated equation

Question 74

turbulence at high velocities and reynold’s number

Answer 74

if nice laminar streamline flow use Poiseuille’s law

but how do you know when have a nice laminar flow? what determines when layers of fluid become turbulent, eddy currents etc

= can predict using Reynold’s nmebr critcal speed that if fluid flows faster than this speed flow becomes turbulent, take reynold’s numebr R X eta/ 2X density X radius of tube

gives you first speed expect turbulence

V= R eta/ 2 X rho X r

for blood reynold’s numebr is around 2000, unitless dimensionless quantity, knowing reynolds numebr gives you want to predict first speed will have turbulence**

Question 75

bile

Answer 75

• if bile prsent in urine can detect its presence because it lowers surface tension of urine so test if liver is metabolizing things the way it should**

another application of surface tension with tent getting raid drops on it, most tents prevent water from seepign through but as soon as touch it may break surface tension adn then water will drip into your tent from where it was so dont break surface tension on tent*

Question 76

soap

Answer 76

breaks surface tension of water, which means water moelcules do nto clump together as much, if not clumpign together can get into small cracks whick kicks out dirt in yoru hands and water bable to better get into cracks where it needs to do

so due to cohesion of water molecules!

Question 77

venturi effect

Answer 77

• water keeps flowing but will start flowing faster through constricted (tgither tube region) because certain amount of fluid flowing through pipe, same volume from bit part of tube has to go through small tube in same time, but only way that is posisble is for front surface to change its shape and travel from small tube beginnign to end in like 1/4 of a second
• volume flwo rate has to stay the same!! so volume per time has got to be the same through another region of the pipe becuase the water has got ot go somehwere! doesnt just disappear so that means water flows faster through constricted region, sometimes much faster! the smaller the radius is compared to original radius the faster the fluid will flow here, why do we care? faster moving fluid means lower pressure** if look at B’s equation says P1+ rhogh1 + 1/2rhov1^2= P2 + rhogh2+ 1/2 rhov2^2
• if assume h are the same so o, so if some pressure of wate rat P1 then at point 2 know velocity is bigger has to be becuse volume flow rate has to stay the same, so it is bigger, but we know the whole thing equals the other, so if you are increasing 1/2 pv2^2 then pressure has to dec get the same!
• B’s principle= when fluid speeds up pressure dec****** fast moving fluid actually has a smaller pressure due to Bernoulli’s equation, what causes venturi effect referring to fact if have tube want smaller pressure region,w ant pressure to drop just cause a narrow constriction in that tube, in that narrow constriction faster moving fluid and lower the pressure***
• so B’s effect for cosntriction in pipe get lower pressure**

Question 78

According to your understanding of Bernoulli’s principle and continuity equation, which of the following statements accurately describes the phenomenon of vascular flutter which occurs when an artery becomes constricted due to the accumulated plaque in its inner walls?

Answer 78

• Vascular flutter occurs when plaque accumulates and constricts an artery, and due to this constriction, the blood has to to flow at a faster rate through the narrowing. This is according to the continuity equation.
• Bernoulli’s principle tells us that the faster the fluid travels, the lesser the pressure of that fluid at that same point.
• If the rate is sufficiently high, the artery will collapse at the region of the plaque and stop blood flow temporarily. Without the flow of blood, there is no Bernoulli effect and the artery will open up again due to arterial pressure. therefore= The constriction causes the pressure to drop and the vessel to collapse.

Question 79

Which of the following statements best describes the hydrodynamic parameters in the Venturi tube diagram below?

Answer 79

The continuity equation is the following: p1A1v1=p2A2v2. According to the continuity equation, velocity is greatest where cross-sectional area is smallest. B’s princple is the following equation: P1+ 1/2p1v1^2 + p1gh1 = P2 + 1/2 p2v2^2 + p2gh2, so according to Bernoulli’s princiople, pressure is greatest where the velocity is the smallest.

At point B, the area is lesser, so the velocity is greater, and then the pressure is lesser. The water level will be higher at B because the pressure is less and fluid travelst the fastest there.

Question 80

A tank with height y is filled with water to the top and is placed at a height z above the ground. Currently the water level is 3.0 meters above the ground. At the bottom of the tank, there is a hole where the water can flow out when needed. Which of the following would increase the flow rate?

Answer 80

=Increase the size of the hole, b/c to inc flow rat ened to inc volume nad that is only way to do it!

To increase flow rate (Q), the volume passing through the aperture must increase.

Decreasing the size of the hole is reminiscent of the continuity equation. However, the equation implies conservation of mass, so more volume would not come through.

with Bernouille’s equation, v= squareroot [2g (h1- h2)]. Ultimately to change the velocity is to change the distance between the top and the bottom of the water.

If we increase z, then according to Bernoulli’s, the distance between the top and bottom remains the same.

If we increase y and z, the tank is higher above the ground and becomes taller, but the distance between the top and bottom remains the same.

Only by increasing the size of the hole would there be more flow rate.

Question 81

When a pitcher throws the baseball and releases it with spin, depending upon the orientation of this spin, the ball will “break” in some direction. In other words, a breaking ball is a pitch that does not travel straight like a fastball as it approaches the batter. Which of the following scenarios accurately describes the phenomenon of “breaking”?

Answer 81

A baseball moving to the right and spinning vertically counterclockwise will experience an upward lift.

A baseball moving to the right will have the streamlines moving to the left around it and vice versa.

If the baseball is spinning vertically, according to Bernoulli’s, it will either experience an upward or downward lift, not leftward or downward. Only if the baseball is spinning horizontally can it experience a leftward or rightward shift.

If the ball is moving to the right, the streamlines are moving to the left. By spinning counterclockwise, the spin and the streamlines match up to create a greater velocity on the top, but they cancel each other out on the bottom for a lesser velocity.

Difference in velocity will result in difference in pressure.****

The baseball will experience a lower pressure on the top with the increased velocity and higher pressure from below with the reduced velocity, and hence the ball will experience an upward lift.

Question 82

Which of the following describes the most realistic shape of middle-sized raindrops as they fall through the Earth’s atmosphere?

Answer 82

“hamburger bun”-like due to air pressure

In deciding on the shape of the raindrop, there are two forces at play here: the surface tension holding the droplet together and the air pressure pushing from below against the bottom surface of the droplet.

Spherical is the most ideal shape achieved by surface tension to minimize surface area, but that shape is maintained for only small droplets.

While teardrop-shaped is the shape promoted by popular culture and used in weather forecasts, small raindrops will be spherical due to surface tension.

Circular is a 2-dimensional shape and would make the raindrop a flat disc.

Flattened on the bottom and with a curved dome on top, the medium-sized raindrop takes on a hamburger bun shape due to the pressure pushing up against the bottom distorting its shape.

Question 83

Which of the following is NOT a characteristic of liquid with laminar flow?

A. low velocity

B. presence of eddies

C. high viscous forces

D. little lateral mixing

Answer 83

EDDIES

Laminar flow is where the fluid flows in layers or lamina without much mixing of the layers. Within each layer, the velocity, pressure, and other hydrodynamic properties remain unchanged.

Laminar flow occurs when the velocity is low or the fluid is very viscous.

Laminar flow is characterized by smooth constant fluid motion, low velocity, high viscous forces, and little lateral mixing. Turbulent flow is characterized by eddies, vortices, and other flow disturbances.

Question 84

According to the Poiseuille’s Law, which of the following statements correctly describes blood flow through arteries?

Answer 84

5

Here are our core equations:Q = \DeltaΔdeltaP/R, R =8\etaη\etaL/\piπpir^44start superscript, 4, end superscript, so =Vasodilation by 20% will double the blood flow rate.

Q=ΔdeltaP/R, R= 8ηL/ πr⁴. Volume flow rate (Q) is proportional to the radius raised to the fourth (r⁴).

Vasoconstriction by 20% can expressed as 0.8. Its effect on the blood flow rate is (0.8)^4, which is 0.4. To reduce the blood flow rate by a factor of 8 would mean 0.125.

If the original flow rate is 100 cm^3/sec, doubling the radius will increase the flow rate to 1600 cm^3/sec since 2^4 = 16.

Resistance is inversely proportional to the radius to the fourth and also to volume flow rate.

Vasodilation by 20% can be expressed as 1.2. Its effect on the blood flow rate would be (1.2)⁴, which is approximately 2.0.

Question 85

Blood takes about 1.0 seconds to pass through a 1.0 millimeter long capillary in the human circulatory system. If the diameter of the capillary is 8.00 μm and the pressure drop is 2.0 kPa, what is the viscosity of the blood, assuming laminar flow?

Answer 85

Use Poiseuille’s law to relate pressure drop to the vessel radius, vessel length, blood flow rate, and blood viscosity: delta P= 8nL/pier⁴Q = (pier⁴ delta P/8LQ)

volume flow rate is Q= Av, where Q= pier2v

plug into original equation to get= r² delta P/ 8Lv

convert all units and watch out for exponents: = (4 x10^-6 m)² (2.0 x 10³ Pa) / 8 (1 x 10^-3 m) (1 x 10^-3m/s)

= (16 x10^-12 m) X (2.0 x 10³ Pa)/ 8 (1 x 10^-6 m X m/s)

= (32 X 10 ^-9 m)/ (8 x 10^-6 m/s) = 4 x 10^-3 Pa X s or 4 mPaXs

Question 86

Which of the following expressions is representative of total power output? (Q = volumetric flow rate, P = pressure)

Answer 86

Pressure (P) has units of N/m², volumetric flow rate (Q) has units of m³/s, volume (V) has units of m³, and time (t) has units of s.

Power has units of W or J/s, and joule is N·m.

Starting from N/m²2, multiply by volume (m³) and divide by time (s):

(N/ m²) X (m³) X (1/s) = N·m

PQ would be the same as multiplying by volume and dividing by time.