Chapter 4: Fluids Flashcards
What is a fluid?
Fluids are characterized by their ability to flow and conform to the shapes of their containers. Both liquids and gases are fluids.
What is density? What is the equation for density? What are the SI units for density? What is the density of water in cm^3 and m^3? How many liters are in a cubic meter?
Density is the ratio of mass to volume. Density is a scalar quantity and therefore has no direction.
How can the weight of any volume of a given substance with known in density be calculated?
The weight of any volume of a given substance with a known density can be calculated by multiplying the substances density by its volume and the acceleration due to gravity. This is a calculation that appears frequently when working through buoyancy problems on test day.
We can work this out with dimensional analysis as done in the picture. Make sure to be comfortable doing this to really understand how to calculate weight with known density and volume.
What is specific gravity? What is the equation for specific gravity?
What will an object do when placed in water that has a specific gravity greater than one? What will an object do in place in water that has a specific gravity less than one?
Specific gravity is a ratio of a density over the density of water. It is a unit number that is usually expressed as a decimal. The specific gravity can be used as a tool for determining if an object will sink or float in water.
Specific gravity example page 129
We got stuck on this problem due to dimensional analysis.
Couple things to realize:
The density of water is 1000 kg kilograms per meter cubed. By knowing this weekend, change the density of water in the denominator to kilograms per meter cubed.
We could also express the density of benzene in grams per centimeter cubed instead of kilograms per meter cubed.
The density of benzene is 877 kg/m³. What is the density of benzene in grams per centimeter cubed?
What is the density of water in kilograms per liter, in kilograms per meter cubed?
How do you convert centimeters cubed to meters cubed?
What is pressure? What is the equation for pressure? What are the SI unit units for pressure? Is pressure a scalar or vector quantity?
Pressure is a ratio of the force per unit area. Pressure, like density, is a scalar quantity as it has a magnitude but no direction. The SI unit for pressure is the Pascal (N/m^2).
Time to work units.
What are the units for speed, velocity, acceleration, force, energy, Work, Power, pressure, volume, length, time, temperature, heat, entropy.
What are four commonly used units of pressure? What is the conversion between them?
Pressure is a scalar value as it has magnitude and no direction. Pressure can mistakenly be thought of as a vector. Talk about it.
It is easy to assume that pressure has a direction because it is related to a force, which is a vector. However, note that it is the magnitude of the normal force that is used in pressure calculations (P=F/A).
No matter where one positions a given surface, the pressure exerted on that surface within a closed container will be the same, neglecting gravity.
For example, if we placed a surface inside a closed container filled with gas, the individual molecules, which are moving randomly within the space, will exert pressure that is the same at all points within the container. Because the pressure is the same at all points along the walls of the container, and within the space of the container itself, pressure applies in all directions at any point and, therefore, is a scalar rather than a vector.
Of course, because pressure is a ratio of forced to area, when unequal pressures are exerted against objects, the forces acting on the object will add in vectors, possibly resulting in acceleration.
Example on pressure difference page 130
We can rearrange the equation for pressure to solve for net force.
Be careful when we’re dealing with units. We need to go from atmosphere to Pascal somewhere along the equation. I naturally did it at the end, but only realized when I did not come up with the same answer the book did until I converted my final answer to Pasca. (1atm = 10^5 Pa)
What is absolute (hydrostatic) pressure? What is the equation for absolute pressure?
Absolute pressure is the total pressure that is exerted on an object that is submerged in the fluid.
A useful way to remember the two parts of the absolute pressure equation is to think of diving into a swimming pool. At the surface of the water, the absolute pressure is usually equal to the atmospheric pressure (Po). You dive into the pool, the water exerts an extra pressure on you (pgz), in addition to the surface pressure.
What is gauge pressure? What is the equation for gauge pressure?
Gauge pressure is the difference between the absolute pressure and atmospheric pressure.
When you check a tire, the gauge pressure is the difference between the absolute pressure inside the tire and the atmospheric pressure outside the tire. In other words, gauge pressure is the amount of pressure in a space above and beyond atmospheric pressure.
What happens to gauge pressure when atmosphere pressure equals ambient (incident) pressure?
When atmospheric pressure equals incident (ambient) pressure, then gauge pressure equals (rho)gz at depth z.
Gauge pressure at depth and absolute pressure example page 132
When ambient pressure equals atmospheric pressure, then gauge pressure equals (rho)gz.
The absolute pressure in this circumstance will be equal to the gauge pressure plus the atmospheric pressure.
MCAT concept check 4.1 page 132 question 1
How does gauge pressure relate to the pressure exerted by a column of fluid?
Gauge pressure is equal to the pressure exerted by a column of fluid plus the ambient pressure above the fluid, minus atmospheric pressure. When atmospheric pressure is the pressure above the fluid column, then gauge pressure equals the fluid pressure.
MCAT concept check 4.1 page 132 question 2
What is the relationship between weight and density?
Weight is density times volume and acceleration due to gravity.
MCAT concept check 4.1 page 132 question 2
What is the relationship between weight and density?
Weight is density times volume and acceleration due to gravity.
MCAT concept check 4.1 page 132 question 3
What is the SI unit for pressure? What are other common unit units of pressure? What is the conversion between these pressures?
What is hydrostatics? What is Pascal’s principal? Where do we see the application of Pascal’s principal in our studies?
Hydrostatics is the study of fluids at rest and the forces and pressure pressures associated with standing fluids.
Pascal’s principal states that for fluids that are incompressible, a change in pressure will be transmitted undiminished to every portion of the fluid into the walls of the containing vessel.
We see application of Pascal principal in hydraulic systems.
In a hydraulic lift, how can Pascal’s principle be applied in an equation?
On the left side of the lift, there is a piston of cross-section area A1. When the piston is pushed down the column, it exerts a force with a magnitude equal to F1 and generates a pressure equal to P1. The piston displaces the volume of liquid equal to A1d1 (the cross-sectional area times the distance gives a volume). Because the liquid inside is incompressible, the same volume of fluid must be displaced on the right side of the hydraulic lift, where we find a second piston with a much larger surface area, A2. The pressure generated by piston one is transmitted undiminished to all points within the system, including to A2. As A2 is larger than A1 by some factor, the magnitude of the force, F2, exerted against A2 must be greater than F1 by the same factor so that P1 equals P2, according to Pascal’s principal.
There are three equations we can derive from P1 = P2 (Pascal principal), using the following hydraulic lift as a guide. What are those three equations (hint: force, volume, work).
The force supplied is proportional to the area of 1 and 2.
The volume is proportional to the distance the piston travels and the area of 1 and 2.
Work = fdcostheta = PdeltaV, which brings us to work is proportional to the force and distance of 1 and 2.
Again. What are the three equations from Pascal’s principle regarding pressure volume and work?
Again. What are the three equations from Pascal’s principle regarding pressure volume and work?
Hydraulic press example page 135
The question provided a radius and a force. We can use Pascal’s principle and proportion of force and area.
We need to take the radius and calculate the area. Radius of a circle is pi r^2.
What is Archimedes’s principle? What is buoyancy? What is the buoyant force equation?
Archimedes principal deals with the buoyancy of objects when placed in a fluid. The principal states that a body wholly or partially immersed in a fluid will be buoyed upward by a force equal to the weight of the fluid that it displaces.
What is the equation for specific gravity? What does this tell us about the tendency of an object to sink or float?
The density of ice is 0.92 g/cm^3. What is the SG of ice? How much ice will be submerged when placed in water? How much sticking out?
How much of an item with the same density of water be submerged?
Buoyancy example page 137.
Find the answer two ways.
I figured out a super easy way to solve this problem using specific gravity ratio. If 50% of the wood is submerged, then that means its specific gravity is 0.5 compared to whatever fluid it is submerged in.
That being said, it is really important to understand how to work through the forces of this question and I should be familiar with it.
The average density of a human being is about 985 kg/m^3.
Speak about this in terms of the density of pure water and the density of saltwater.
A wooden block floats in the ocean with half its volumes submerged. Find the density of the wood.
(Density of seawater is 1025 kg/m^3)
The buoyant force equals the weight of the block.
The weight of the block is equal to the mass of the block times acceleration due to gravity, and also equal to the density of the block times the volume of the block times the acceleration due to gravity.
The buoyant force is equal to mass of the water times acceleration due to gravity, and is also equal to the density of water times of volume of water times the acceleration due to gravity.
The final trick here is realizing that the volume of water equals the volume of the block of wood divided by two.
How to large ships stay afloat?
Any object will float if its average density is less than that of water. The whole of a ship would sync by itself, but all the air submerged beneath the water level, between the ships, lower decks, lowers the ships average density to be less than that of water. Duh.
What is surface tension? What causes surface tension?
Surface tension causes a liquid to form a thin but strong layer like a skin at the liquids surface. Surface tension results from cohesion, which is the attractive force that a molecule of liquid feels towards other molecules of the same liquid. On the surface, molecules only have strong attractive forces from the molecules below them, which pulls the surface of the liquid toward the center. This establishes tension in the plane of the surface of the water; when there is an indentation on the surface (like the foot of a water strider) then the cohesion can lead to a net upward force.
What is cohesion? What is adhesion?
Cohesion is the attractive force that a molecule of liquid feels toward other molecules of the liquid.
Adhesion is the attractive force that a molecule of the liquid feels toward the molecules of some other substance.
What causes a meniscus of a fluid to concave? What causes a meniscus to convex? Which is more common?
Where should measurement be made for either circumstance?
When cohesive forces are stronger than adhesive forces, the meniscus will convex. (Fluid crawls up the sides of the container)
When cohesive forces are weaker than adhesive forces, the meniscus will be concave. (Liquid level higher in the middle than the edges)
Convex meniscus are more common.
What causes a meniscus of a fluid to concave? What causes a meniscus to convex? Which is more common?
Where should measurement be made for either circumstance?
When cohesive forces are stronger than adhesive forces, the meniscus will convex. (Fluid crawls up the sides of the container)
When cohesive forces are weaker than adhesive forces, the meniscus will be concave. (Liquid level higher in the middle than the edges)
Convex meniscus are more common.
MCAT concept check 4.2 page 139 hydrostatics question 1 and 2.
MCAT concept check 4.2 page 139 hydrostatics question 3
MCAT concept check 4.2 page 139 hydrostatics question 4
MCAT concept check 4.2 page 139 hydrostatics question 5
What is fluid dynamics?
Fluid dynamics is the study of fluids and motion.
What is viscosity? What is viscous drag? What is the SI units for viscosity?
Viscosity is the resistance of a fluid to flow. Increased viscosity of fluid increases its viscous drag, which is a non-conservative force that is analogous to resistance.
Why do low viscosity fluids behave like ideal fluids? What is the term for fluids that have no viscosity?
Low viscosity fluids have low internal resistance to flow and behave like ideal fluids. Assume conservation of energy in low viscosity fluids with laminar flow.
Fluids that have no viscosity are called inviscid.
More viscous fluid will “lose” more energy to nonconservative forces.
Viscosity should be assumed negligible on test day.
What is laminar flow? What is turbulent flow?
Laminar flow is smooth and orderly. Modeled with layers of fluid that flow parallel to each other.
Turbulent flow is tough and disorderly. Turbulence causes the formation of eddies, which are swirls of fluid of varying sizes occurring typically on the downstream side of an obstacle.
What is Poiseuille’s law?
For fluid flowing through a tube with diameter D, critical speed (vc) can be calculated how?
What is the continuity equation (regarding fluid flow)? What kind of understanding can be established from the continuity equation?
What’s in the top image is a fluid within an invisible tube as it passes from P to Q. Flow rates at point P and point Q are the same, however, the linear speed is faster at P.
This is essentially an expression of conservation of matter: if X liters of fluid pass a point and a given amount of time, then X liters of fluid must pass all other points in the system in the same amount of time.
We can clearly state, without any exceptions, that flow rate (volume per unit time) is constant for a closed system and is independent of changes in cross-sectional area.
This leads us to the continuity equation, which tells us that fluids will flow more quickly through narrow passages and more slowly through wider passages.
What is the continuity equation?
The continuity equation arises from the conservation of massive fluids.
What is Bernoulli’s equation?
Ask KC about this equation. I want to really understand it well. Absolute pressure, dynamic pressure, static pressure.
First, the flow rate within a closed space must be constant in all points (demonstrated by the continuity equation).
Second, fluids that have low viscosity and demonstrate laminate flow can also be approximated to be conservative systems: the total mechanical energy of the system is constant if we discount the small viscous drag forces that occur in all real liquids.
Combining these principles of conservation gets us to the Bernoulli’s equation.
Bernoulli’s equation states that the sum of the static pressure and dynamic pressure will be constant with a closed container for an incompressible fluid, not experiencing viscous drag.
How is Bernoulli’s equation a statement of energy conservation?
More energy dedicated toward fluid movement means less energy dedicated towards static fluid pressure. The inverse of this is also true: less movement means more static pressure.
The faster a fluid moves, the lower pressure it will have.
What is a Venturi flow meter? What is the Venturi effect?
How do airplanes get lift?
What is dynamic pressure and static pressure in the Bernoulli equation?
Something to ask KC. So if velocity increases, dynamic pressure increases greatly, static pressure decrease decreases.
I’m finding this counterintuitive because faster moving fluids exert less pressure.
Continuity equation in Bernoulli equation example page 146
First, we used the continuity equation to solve for the cross-sectional area at the bathroom.
We then use Bernoulli’s equation to solve for the pressure required at ground level.
This equation is cumbersome but worthwhile in doing multiple times as to become comfortable with continuity equation in Bernoulli’s equation.
MCAT concept check page 147 fluid dynamics question 1
MCAT concept check page 147 fluid dynamics question 2
MCAT concept check page 147 fluid dynamics question 3
Circulatory system paragraph from book
Respiratory system paragraph from book
MCAT concept check fluid fluids in physiology page 149 question 1
MCAT concept check fluid fluids in physiology page 149 question 2
MCAT concept check fluid fluids in physiology page 149 question 3
More on Fluids in Physiology page 152
MCAT mastery on fluids chapter 4 page 122 question 1
The thing about this question is to really understand gauge pressure. Gauge pressure is ambient pressure (pressure at the surface) minus atmospheric pressure.
P = absolute pressure: total pressure exerted on object submerged in fluid.
(P = Po+(rho)gz)
Po = incident or ambient pressure (pressure at the surface)
Patm = atmospheric pressure
IF ATMOSPHERIC PRESSURE AND INCIDENT PRESSURE ARE EQUAL, THEN GAUGE PRESSURE EQUALS (rho)gz
Where rho is density of fluid, g is acceleration due to gravity, Z is depth of the object.
MCAT mastery on fluids chapter 4 page 122 question 2
Two ways to solve this problem: do the calculation or absorb the problem and use your intuition and know how regarding buoyancy forces.
We could quickly solve this problem on test day by recognizing that the answer choices contain an outlier (A), value slightly less than the weight of the anchor (B), the weight of the anchor (C), and the value slightly higher than the weight of the anchor (D). Since buoyant force is in the same direction as tension and their sum must equal the weight of the anchor, (B) is the most likely answer.
Math way:
MCAT mastery on fluids chapter 4 page 122 question 3
MCAT mastery on fluids chapter 4 page 122 question 4
This question uses the continuity equation: V1A1=V2A2
Be cognizant these problems often diameter, or radius, and I need area in the continuity equation. The equation for the area of a circle is pi r squared or pie d squared over four. Pie D squared over for method done in orange in image.
Got a little stuck on the algebra here when I was faced with a whole number multiplied by a fraction squared. Remember that if you score a fraction, you square the numerator and the denominator.
MCAT mastery on fluids chapter 4 page 122 question 5
MCAT mastery on fluids chapter 4 page 122 question 6
Venturi effect: for a horizontal flow, there is an inverse relationship between pressure and speed, and in a closed system, there is a direct relationship between cross-sectional area and pressure exerted on the walls of the tube.
In the picture of fluids flowing through different diameter pipes: as the tube narrows, linear speed increases at point 2 (the narrow part). Thus, pressure exerted at the walls at point 2 decreases, causing the column above point 2 to have a lower height.
MCAT mastery on fluids chapter 4 page 122 question 7
You can zoom into the books answer above the whiteboard image.
MCAT mastery on fluids chapter 4 page 122 question 8
MCAT mastery on fluids chapter 4 page 122 question 9
Answer on page 157
I came up with a triangle of relationship between force area and distance based on Pascal’s principle. Does this help you remember it?
MCAT mastery on fluids chapter 4 page 122 question 10
MCAT mastery on fluids chapter 4 page 122 question 11
MCAT mastery on fluids chapter 4 page 122 question 12
MCAT mastery on fluids chapter 4 page 122 question 13
MCAT mastery on fluids chapter 4 page 122 question 14
MCAT mastery on fluids chapter 4 page 122 question 15
Equations from chapter Fluids
