Fluid definition:

has the ability to flow and conform to the shape of the container

Solid definition:

does not flow and its rigidity helps it retain a shape independent of that of any container

Liquids and gases are both:

fluids

Density equation:

p = ^{m}/_{v}

a scalar quantity; units = ^{kg}/_{m3} or ^{g}/_{mL} or ^{g}/_{cm3}

How many liters are in a cubic meter?

1000

Equation to determine the weight of any volume of a given substance:

W = ρVg

where p is the density and V is the volume of the substance

Specific gravity:

the ratio of the density of a substance to that of pure water at 1 atm and 4 degrees Celsius; if it is less than one the object will float; if it is greater than one the object will sink

Density of water:

1,000 ^{kg}/_{m3} or 1 ^{g}/_{cm3}

Pressure is:

the force per unit of area; it is exerted by a fluid on the walls of its container and on objects placed in the fluid

Equation to determine pressure:

P = ^{F}/_{A}

where F is the normal force and A is the area; a scalar quantity; units = Pa =^{ N}/_{m2}

Pressure conversions:

1.013 X 10^{5} Pa = 1 atm = 760 torr = 760 mmHg

Absolute pressure is:

the sum of all pressure at a certain point within a fluid; it is equal to the pressure at the surface of the fluid (liquid or gas) plus the pressure due to the fluid itself

Equation to determine absolute pressure:

P = P_{o} + ρgh

where P is the absolute pressure, P_{o} is the pressure at the surface, and ρgh is (density fluid above)(gravity)(height of submerged object below surface)

units = ^{N}/_{m2}

Gauge pressure is:

the difference between the surface pressure and the absolute pressure

Equation to determine gauge pressure:

P_{g} = P - P_{atm} = (P_{o} + ρgh) - P_{atm}

units = Pa

Forces and fluids:

fluids can exert perpendicular forces, but cannot withstand shear forces

On the MCAT, liquids are assumed to be:

incompressible and are ideal conservative systems

Forces and solids:

solids can exert perpendicular forces and can withstand shear forces

If mass is held constant in the density equation, what is the relationship between volume and density?

inverse

During thermal expansion, what happens to density and volume?

density decreases as volume increases

The pressure exerted by a gas against that walls of its container will always be:

perpendicular to the container walls

Hydrostatics is:

the study of fluids at rest and the forces and pressures associated with standing fluids

Pascal's principle states that:

an applied pressure to an incompressible fluid will be distributed undiminished throughout the entire volume of the fluid; hydraulic machines operate based on this principle

Equation of Pascal's principle for incompressible fluids in containers:

P = ^{F1}/_{A1 }= ^{F2}/_{A2}

V = A_{1}d_{1} = A_{2}d_{2}

W = F_{1}d_{1} = F_{2}d_{2}

Area of a piston:

πr^{2}

(the surface of a piston is circular)

Equation to determine the buoyant force on a floating object:

F_{buoy} = (V_{fluid displaced})(p_{fluid)}(g) = weight of the object

units = (kg)(^{m}/_{s2})

Equation to determine the buoyant force on a fully submerged object:

F_{buoy} = (V_{object submerged})(p_{fluid})(g)

units = (kg)(^{m}/_{s2})

When an object is placed in a fluid, it will sink until:

the point at which the volume of displaced fluid exerts a force that is equal to the weight of the object

An object's specific gravity represented as a percentage directly indicates:

the percentage of the object's volume that is submerged in the fluid

The direction of buoyant force is always:

opposite the direction of gravity

Surface tension results from:

cohesion (the attractive force that a molecule of liquid feels toward other molecules of the same liquid)

Adhesion:

the attractive force a molecule of liquid feels toward the molecules of some other substance (causes a meniscus)

A meniscus curved upward forms when:

the adhesive forces between the liquid and the container are greater than the cohesive forces of the liquid

A backward meniscus forms when:

the adhesive forces between the liquid and the container are less than the cohesive forces of the liquid

Viscosity is:

the resistance of a fluid to flow; can be thought of as fluid friction; the higher the viscosity, the slower the flow

Low-viscosity fluids have low internal resistance and behave more like:

ideal fluids (which have no viscosity)

SI unit of viscosity:

(N)(^{s}/_{m2})

The two types of fluid flow:

laminar (smooth and orderly) and turbulent (rough and disorderly)

Equation to determine the critical velocity (Vc) of a fluid flowing through a tube:

v_{c} = ^{NRη}/_{ρD}

where N_{R} is a given constant; η is the viscosity of the fluid, ρ is the density of the fluid, and D is the diameter of the tube

units = ^{m}/_{s}

Streamines:

indicate the pathway followed by fluid particles as they move; velocity vector always tangentil to streamline; streamlines never cross each other

For a closed system, the volumetric rate of flow is:

constant and independent of changes in cross sectional area (the amount of water flowing past a point in a given amount of time is constant regardless of the width of the tube)

Fluids move more quickly through --- passages and more slowly through --- passages.

more quickly through narrow passages and more slowly through wider passages (continuity equation)

The continuity equation:

v_{1}A_{1} = v_{2}A_{2} = constant (the rate of flow)

Bernouli's equation (an expression of conservation of energy for a flowing fluid):

P_{1} + ^{1}/_{2}ρv_{1}^{2} + ρgy_{1} = P_{2} + ^{1}/_{2}ρv_{2}^{2} + ρgy_{2}

For horizontal flow, there is an inverse relationship between:

pressure and velocity

Elasticity of solids:

a measure of the response of a solid to an application of pressure; depending on the particular way in which the pressure is exerted, the object may experience a change in length, volume, or lateral displacement known as shear

Stress on a solid is:

a measurement of the pressure (F/A) applied to the solid

Strain on a solid is:

the degree to which the solid deforms under pressure

Equation to determine Young's Modulus (perpendicular application of force):

Y = ^{(F/A) }/_{ (∆L/L)}

it gives the change in length of a solid when a pressure is applied perpendicularly to it (compression or stretching)

Elastic limits of a solid:

the degree to which an object can be compressed or stretched before it is permanently deformed or ruptured

Yield strength of a solid is:

the point of shape change beyond which a material will not return to its original dimensions once the applied force is removed

Ultimate strength of a solid is:

the point at which enough stress is applied to a solid object that it ruptures

Equation to determine Shear Modulus (parallel application of force):

S = ^{(F/A) }/ _{(x/h)}

where x is the lateral displacement and h is the vertical displacement

In both Young's modulus and Shear modulus, the ratio is:

^{(stress)} / _{(strain)}

stress is always represented as pressure (F/A)

Equation to determine Bulk modulus (chage in volume due to pressure):

B =^{ (F/A) }/ _{(∆V/V)}

where V is volume

Relationship between the speed of sound and the Bulk modulus:

the speed of sound is proportional to the square root of the bulk modulus; sounds travel fastest through solids (highest bulk modulus) and slowest through gases (lowest bulk modulus)

Bernoulli's equation states the the sum of --- and --- will be constant between any two points in a closed system.

static pressure and dynamic pressure