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Flashcards in Fluids Deck (56)
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1
Q

What is a fluid?

A

A fluid is a phase of matter that is capable of yielding to pressure and changing its shape to fit a container.

On the MCAT, fluids come in two forms: liquids and gases.

2
Q

What are the properties of an ideal fluid?

A

An ideal fluid:

  • is incompressible
  • is non-viscous (no friction)
  • changes shape to fit its container
  • flows without turbulence

On the MCAT, all fluids are assumed to be ideal unless otherwise noted.

3
Q

What term is given to fluid flow that lacks turbulence?

A

Fluid flow that is not turbulent is known as laminar flow. Ideal fluids are assumed to be laminar.

When a fluid molecule is moving in a laminar pattern, its motion is orderly and occurs in the same direction as neighboring molecules.

4
Q

Water is flowing through a level pipe of uniform diameter. What can be said about the nature of its flow?

A

Since water can be assumed to be an ideal fluid, the flow will be frictionless and non-turbulent.

The speed of the flow will be constant at all points along the pipe, and the pressure on the walls of the pipe will be constant at all points.

5
Q

Define:

density (ρ)

A

A substance’s density (ρ) is the mass per unit volume of that substance. Put in other words, density equals mass over volume.

The SI units for density are kg/m3. Other units may appear on the MCAT, such as g/cm3 or g/mL.

6
Q

What units of density are most commonly used?

A

Common measures of density include g/cm3, g/mL, kg/L, and kg/m3.

The first three of the above values are equivalent in magnitude. The last value, kg/m3, differs by a factor of 1000.

7
Q

What is the density of water in g/cm3 and g/mL, respectively?

A

Since 1 cm3 approximately equals 1 mL, the density of water is the same for both sets of units: 1 g/cm3 and 1 g/mL.

The density of water in various units should be memorized for the MCAT.

8
Q

What is the density of water in kg/m3 and kg/L, respectively?

A

The density of water is 1000 kg/m3 and 1 kg/L.

The SI units for density are kg/m3. The density of water in various units should be memorized for the MCAT.

9
Q

Define:

specific gravity

A

A substance’s specific gravity is that substance’s density in comparison to the density of water.

The magnitude of a substance’s specific gravity is identical to the substance’s density as expressed in g/mL. However, specific gravity is a unitless quantity.

10
Q

Define:

buoyancy

Please provide the definition of buoyancy, not the formula for buoyant force (that’ll come later)!

A

Buoyancy is the tendency of an object to weigh less when partially or fully submerged in a fluid.

Buoyancy is generated by the fluid displaced by the object. The fluid pushes up on the object with a force equal to the weight of the fluid displaced.

11
Q

How is the buoyant force of a submerged object calculated?

A

The buoyant force of a submerged object is simply the weight of the fluid displaced by the portion of the object that is submerged.

FB = (ρfluid)(Vsub)(g)

Where:

  • FB = buoyant force pushing up on the object (N)
  • ρfluid = density of the liquid (kg/m3)
  • Vsub = volume of the object submerged in the liquid (m3)
  • g = 10 m/s2
12
Q

An object with a volume of 1.5 L is fully submerged in water. What is the buoyant force on the object?

A

The buoyant force on the object is 15 N.

Using the definition of buoyant force:

FB = (ρfluid)(Vsub)(g)
FB = (1 kg/L)(1.5 L)(10 m/s2)
FB = 15 N

13
Q

Equivalent objects are submerged in ethyl alcohol (ρ = 0.79 kg/L) and mercury (ρ = 5.43 kg/L). Which object experiences the larger buoyant force?

A

The object submerged in mercury will experience the larger buoyant force.

The buoyant force is equal to (ρfluid)(Vsub)(g). Since the objects are identical, the submerged volume is equal in the two cases, as is the value of g. The fluid with the larger density must then produce the higher buoyant force.

14
Q

If a solid object is dropped into a liquid, under what conditions will it float?

A

The object will float if its density is less than or equal to the density of the surrounding liquid.

Otherwise, the object will sink.

15
Q

What information can be discerned from the effective weight of a submerged object?

A

The effective weight of an object submerged in a fluid is equal to the object’s weight on dry land minus the buoyant force. If the weight on land and the effective weight are known, buoyant force can be calculated.

Weff = mobjg - (ρfluid)(Vobj)(g)

Where:

  • mobj = mass of object (kg)
  • ρfluid = density of fluid (kg/m3)
  • Vobj = volume of object (m3)
  • g = 10 m/s2
16
Q

An aluminum ball with a density of 3 g/cm3 has a mass of 9 kg. What is its effective weight when it is submerged in water?

A

The ball’s effective weight is 60 N.

With a mass of 9 kg and a density of 3 g/cm3, the ball’s volume must be 3000 cm3, or 3 L. It will then displace 3 L of water when submerged. The buoyant force is simply the weight of 3 L of water:

FB = (ρliq)(Vsub)(g)
(1 kg/L) (3 L) (10 m/s2) = 30 N

With a mass of 9 kg, the ball’s weight on land is 90 N. Subtracting the buoyant force yields the final answer, 60 N.

17
Q

A plastic ball with a density of 2 g/cm3 has a mass of 6 kg. What shortcut can help calculate the effective weight of the ball when it is submerged in water?

A

The proportion of the object’s weight cancelled by the buoyant force is exactly equal to the ratio of the fluid’s density to the object’s density.

In this case, water has half the density of the object. Thus, the proportion of the object’s weight cancelled by buoyancy is one-half of the object’s dry land weight.

With a mass of 6 kg, the object’s dry land weight is 60 N. Half of that amount (30 N) is cancelled by buoyancy, so the remaining effective weight is 60 - 30 = 30 N.

18
Q

Define:

Pascal’s Law

A

Pascal’s Law states that a fluid will carry pressure undiminished. In other words, pressure exerted on any part of a fluid will be carried equally to all walls of the container.

Pascal’s Law is most commonly tested on the MCAT using hydraulic lifts.

19
Q

What does Pascal’s Law predict about the pressure on Plates 1 and 2 in the diagram below?

A

Pascal’s Law predicts that the pressures will be equal.

The force (F1) will exert a pressure (P1) on the fluid behind Plate 1. The fluid will exert that pressure, undiminished, on all the walls that it contacts, including Plate 2.

20
Q

In the hydraulic lift pictured below, how does the force F2 change if Plate 2 doubles in area?

A

The force F2 doubles.

According to Pascal’s Law, the pressures on Plates 1 and 2 must be equivalent. From the definition of pressure:

P1 = F1/A1 = F2/A2 = P2

So, force and area are directly proportional, and doubling A2 will double F2 as well.

21
Q

In the hydraulic lift pictured below, how does the distance D2 compare to the distance D1 if Plate 2 is double the area of Plate 1?

A

D2 = ½D1

Since the liquid between the plates in incompressible, the volume displaced by Plate 1 must be equal to the volume displaced by Plate 2:

V1 = A1D1 = A2D2 = V2

So, distance and area are inversely proportional, and a plate with double the area will move half of the distance.

22
Q

Define:

hydrostatic pressure

A

Hydrostatic pressure is the pressure exerted on a submerged object by the fluid in which the object is submerged.

Hydrostatic pressure increases proportionately with the distance beneath the surface of the liquid.

23
Q

What pressure is exerted on an object submerged a distance z below the surface of a liquid?

A

Hydrostatic pressure, often called gauge pressure, is calculated as:

PH = (ρfluid)(g)(z)

Where:

PH = hydrostatic pressure (Pa)
ρfluid = density of the fluid (kg/m3)
g = 10 m/s2
z = distance beneath the liquid’s surface (m)

24
Q

What is the difference between the gauge pressures at a depth of 20 cm and 50 cm in a large, round-bottomed flask filled with water?

A

The pressure at a depth of 50 cm is 2.5 times the pressure at a depth of 20 cm.

The equation for gauge, or hydrostatic, pressure is PH = (ρfluid)(g)(z), which states that pressure is proportional to depth. Note that pressure is independent of vessel shape; the only variables involved are fluid density and depth beneath the surface.

25
Q

Vessel 1 is filled with water, while Vessel 2 is filled with an unknown fluid. The pressure 10 cm beneath the surface of the liquid in Vessel 2 is 3 times the pressure at a depth of 10 cm in Vessel 1. What is the density of the unknown fluid?

A

The unknown fluid’s density is 3 g/cm3.

Since hydrostatic pressure is measured as PH = (ρfluid)(g)(z), pressure is proportional to fluid density. If the pressure in one fluid is higher than that of a second at equal depths, the density of the first fluid must also be higher, by the same proportion.

26
Q

What property distinguishes an ideal fluid as it flows through a pipe?

A

Ideal fluids undergo laminar flow, a form of motion in which the fluid is flowing at the same speed at all points in the pipe.

This is opposed to turbulent flow, where the fluid can have eddies, vortices, and local disruption to the fluid’s speed and direction of flow.

27
Q

How does the flow of a viscous fluid differ from that of an ideal fluid?

A

Viscous fluid undergoes Poiseuille flow, where the fluid near the walls of the pipe flows much more slowly due to viscous interaction with the walls.

Above a certain fluid speed and pipe diameter, viscous fluids begin to flow turbulently as well.

28
Q

Under what conditions does fluid flow become turbulent?

A

Turbulent flow occurs in non-ideal fluids when the cross-sectional area of the fluid flow becomes large, and when the fluid velocity increases.

For any given system, threshold values of cross-sectional area and velocity exist, but the specifics won’t be tested on the MCAT.

29
Q

How does the speed of a fluid flowing through a pipe change as the diameter of the pipe decreases?

A

As pipe diameter decreases, fluid flowing through the pipe increases in speed.

This is akin to placing your thumb partially over the end of a water hose, causing the water to flow through faster.

30
Q

Water flowing through a pipe reaches a region where the pipe’s cross-sectional area is halved. How does the fluid velocity change in this region of the system?

A

As the area of the pipe is reduced by half, the fluid velocity doubles.

The continuity equation describes the relationship between cross-sectional area and velocity:

A1v1 = A2v2

Where:

A = cross-sectional area of the pipe (m2)
v = fluid velocity (m/s)

31
Q

According to the continuity equation, what value remains constant through all points of the same pipe system?

A

The volume flow rate, sometimes called simply flow rate, remains constant.

The continuity equation states that A1v1 = A2v2. Since area is measured in m2 and velocity is measured in m/s, A*v has units of m3/s. This equation, then, is simply a mathematical way to say that flow rate is constant.

32
Q

Water flowing through a pipe reaches a region where the radius of the pipe increases by a factor of 3. How does the fluid velocity change in this region of the system?

A

The fluid velocity decreases by a factor of 9.

According to the continuity equation (A1v1 = A2v2), cross-sectional area and velocity are inversely proportional.

However, the cross-sectional area of a round pipe is proportional to the square of the radius, so if the radius triples, the area increases by a factor of 9. Therefore, the velocity decreases by the same amount.

33
Q

Define:

surface tension

A

Surface tension is the ability of a fluid’s surface to resist an external force. It can also be thought of as a fluid’s tendency to interact with its own particles.

Surface tension is caused by attractive forces between the molecules of the fluid. It is responsible for the spherical shape of soap bubbles and the ability to skip a stone off the surface of a lake.

34
Q

What properties cause fluids to have high surface tension?

A

Fluids with high intermolecular attractive forces have large surface tension values.

For instance, fluids in which the molecules are bound by hydrogen bonding will have more surface tension than nonpolar fluids, where the molecules are only attracted by dispersion forces.

35
Q

Which fluid has a higher surface tension, water (H2O) or carbon tetrachloride (CCl4)?

A

Water has a higher surface tension.

Water molecules are attracted by hydrogen bonding, while carbon tetrachloride molecules are nonpolar and only attracted by dispersion forces. Hydrogen bonding is a much stronger interaction, and leads to surface tension that is nearly four times as strong.

36
Q

Describe the purpose of Bernoulli’s equation.

A

Bernoulli’s equation relates the pressure exerted by a fluid to its speed and depth. It can be thought of as conservation of energy for fluid systems.

37
Q

What is Bernoulli’s equation?

In other words, please write out (or mentally think of) Bernoulli’s equation and the variables involved.

A

Bernoulli’s equation reads:

P1 + ½ρv12 + ρgh1 = P2 + ½ρv22 + ρgh2

Where:

P = pressure exerted by the fluid (in Pa)
ρ = density of the fluid (in kg/m3)
v = speed of the fluid (in m/s)
h = depth of the fluid (in m)

38
Q

According to Bernoulli’s equation, how does the pressure exerted by a fluid change as its velocity increases?

A

As fluid velocity increases, the pressure it exerts decreases.

Bernoulli’s equation reads:

P1 + ½ρv12 + ρgh1 = P2 + ½ρv22 + ρgh2

Assuming that the depth does not change, the third term on each side is constant and cancels out. If the velocity increases, v2 > v1, meaning that P2 < P1.

39
Q

According to Bernoulli’s equation, how does the pressure exerted by a fluid change as height increases?

A

As height increases, pressure decreases.

Bernoulli’s equation reads

P1 + ½ρv12 + ρgh1 = P2 + ½ρv22 + ρgh2

Assuming a static fluid, or constant velocity, the second term on each side is constant and cancels out. Here, h2 > h1, so P2 must be less than P1.

40
Q

Why do some people put boards on the outside of their windows during a hurricane?

A

During a hurricane, the wind speed increases significantly. According to Bernoulli’s equation, this results in a severe drop in pressure outside the house.

The pressure difference between the inside and outside leads to the danger of the windows being blown out; boards on the outside can prevent this damage.

41
Q

How does the air pressure on top of a mountain compare to that at the base of the mountain?

A

The air pressure on top of the mountain is lower.

Bernoulli’s equation predicts that pressure decreases as height, or altitude, increases.

42
Q

Define:

solid

A

A solid is an object of a particular shape and volume, neither of which change in the absence of external forces.

43
Q

What are the properties of an ideal solid?

A

An ideal solid is:

  • perfectly elastic
  • smooth
  • homogenous
44
Q

An ideal bar of iron is exposed to an external force, which causes it to flex. What happens to its shape when the force is released?

A

The bar assumes the same shape it held before it was exposed to the force.

Since ideal solid objects are perfectly elastic, they can be deformed in any way and will return to their original shape.

45
Q

Define:

elastic limit

A

A solid’s elastic limit is the maximum force to which it can be exposed and still return to its original shape.

An object which is exposed to a force greater than its elastic limit will be permanently deformed. Different substances have different elastic limits.

46
Q

Define:

coefficient of thermal expansion

A

An object’s coefficient of thermal expansion is a measure of how much the object’s size changes due to temperature change.

Most objects expand when they are heated, and shrink when they are cooled.

47
Q

What formula describes how the length of an object changes when its temperature changes?

A

An object’s length change is given by the following equation:

ΔL/L =αL ΔT

Where:

L = object’s original length (m)
ΔL = change in the object’s length (m)
αL = object’s coefficient of thermal expansion (1/K)
ΔT = change in temperature (K)

48
Q

What is stress, as it refers to a solid?

A

The stress felt by a solid object is defined as the force it is subjected to divided by the area over which that force is exerted.

Stress has SI units of N/m2, identical to the units of pressure, and can be thought of in a similar fashion.

49
Q

What is strain, as it refers to a solid?

A

Strain is the change in length of an object that is placed under stress. Strain is defined as the change in length divided by the original length, or ΔL/L.

Since strain is given in units of length/length, it is a unitless quantity.

50
Q

What information can be discerned from the modulus of a solid?

A

The modulus of a solid is a measure of how resistant the solid is to stress. The higher the modulus, the less the solid changes (with respect to volume, for example) when stressed.

Of the several kinds of modulus for a given solid, all are defined as stress divided by strain.

51
Q

Define:

Young’s modulus

A

Young’s modulus is the modulus that measures a solid’s response to a compressive force (one that makes the object shorter).

As with all moduli, Young’s modulus is defined as stress divided by strain. In this case, the stress is a compressive force, and the strain is the proportional length change under compression.

Y = (F/A)/(ΔL/L)

52
Q

By what proportion is a bronze bar compressed when it is exposed to a stress of 10 MPa?

The Young’s modulus of bronze is 100 GPa.

A

The bar is compressed by 0.01% of its original length.

Young’s modulus is defined as:

Y = stress/strain
100 x 109 Pa = 10 x 106 Pa / strain
strain = ΔL/L = 10-4

53
Q

Define:

shear forces

A

A shear force is a force exerted parallel to the surface of an object. It causes the object to temporarily deflect sideways in response to the stress.

54
Q

Define:

shear modulus

A

Shear modulus is the modulus that measures a solid’s response to a shear force.

As with all moduli, shear modulus is defined as stress divided by strain. In this case, the stress is a shear force, and the strain is the proportional deflection under shear.

S = (F/A)/(Δx/h)

55
Q

By how much is a 1 m steel cube deflected when it is exposed to a stress of 80 MPa?

The Young’s modulus of bronze is 80 GPa.

A

The steel cube is deflected sideways by 1 mm.

Shear modulus is defined as:

S = stress/strain
80 x 109 Pa = 80 x 106 Pa / strain
strain = Δx/h = 10-3
Δx / (1 m) = 10-3 m

56
Q

A cube of styrofoam with a density of 0.5 g/cm3 is dropped into water, quickly popping back up to the surface. What fraction of the cube will be submerged in the water?

A

One-half of the cube will be submerged.

The proportion of an object submerged is simply equal to ρobjfluid, where ρobj is the object’s density and ρfluid is the fluid’s density. In this case, the object has one-half of the density of the liquid, so one-half of it will be submerged when it floats. Note that if ρobj > ρliq, this fraction will be greater than 1 and the object will sink to the bottom.