density
scalar quantity and therefore has no direction
Hydrostatics
the study of fluids at rest and the forces and pressures associated with standing fluids.
Pascal's principle
*conservation of energy (assuming the absence of frictional forces)
Work due to pressure and volume (fluids)
Bouyant Force (F_{bouy})
A body wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid that it displaces.
F_{bouy}=(V_{fluid displaced}) (ρ_{fluid})g=(V_{object submerged})(ρ_{fluid})(g)
cohesion
the attractive force that a molecule of liquid feels toward other molecules of the same liquid.
adhesion
the attractive force that a molecule of the liquid feels toward the molecules of some other substance
viscosity
resistance of a fluid to flow
 *Because viscosity is a measure of a fluid's internal resistance to flow, more viscous fluids will “ lose” more energy to friction.
 The SI unit of viscosity is the newton · second/m^{2} (N· s/m^{2}).
ideal fluids
no viscosity and are described as inviscid.
LAMINAR AND TURBULENT FLOW
Laminar: smooth/orderly
Turbulant: rough and disorderly
Critical Belocity
N_{R }is a dimensionless constant called the Reynolds number, η is the viscosity of the fluid, ρ is the density of the fluid, and D is the diameter of the tube.
V_{c}=N_{R}η /ρD
streamlines.
streamlines indicate the pathway followed by tiny fluid elements (sometimes called fluid particles) as they move.
The velocity vector of a fluid particle will always be tangential to the streamline at any point.
Streamlines never cross each other.
The Continuity Equation
tells us that fluids will flow more quickly through narrow passages and more slowly through wider ones.
v_{1}A_{1}=v_{2}A_{2}=a constant rate of flow
BERNOULLI'S EQUATION
P_{1 }+ (ρv_{1}^{2})/2 + ρgy_{1} = P_{2} + (ρv_{2}^{2})/2 + ρgy_{2} = a constant
 energy conservation: More energy dedicated towards fluid movement means less energy dedicated towards fluid pressure.
 Newton's second law relates forces and accelerations: When two points within a fluid are at different static pressures, the fluid will experience a net force from the point of higher pressure to that lower pressure and will flow (and accelerate) in that direction.
Elastic Properties of Solids
a measure of the response of a solid to an application of pressure
Moduli: Youngs, Shear, Builk
For all three moduli, a largenumber represents a more rigid material, while a small number represents a more malleable material.
Young's modulus, Y
the ratio of stress over strain
Y= (F/A)/ΔL/L)
Yield strength is the point of shape change beyond which a material will not return to its original dimensions once the applied force is removed (think of a crumpled piece of paper).
ultimate strength will be reached if more stress applied, beyond which point the object will rupture (think of a broken rubber band).
shear modulus
S= (F/A)/(x/h)
shear: shapre change due to force applied parallel to an object's surface rather than perpandicular to it
bulk modulus
indicates the degree to which a material will experience a change in its volume in relation to an applied pressure
B=(F/A)/ΔV/V)
 speed of sound in a material is proportional to the square root of the bulk modulus of that material.
 Because gases have small bulk moduli, liquids have larger bulk moduli, and solids have the largest, sound will travel fastest through solids and slowest through gases
Gauge Pressure
difference between surface pressure and absolute pressure In liquids, gauge pressure is caused by the weight of the liquid above the point of measurement
Absolute Pressure
is the sum of all pressures at a certain point within a fluid; it is equal to the pressure at the surface of the fluid (usually atmospheric pressure) plus the pressure due to the fluid itself
Pressure

Defined as a measure of force per unit area; 
it is exerted by a fluid on the walls of its container and on objects placed in the fluid
It is a scalar quantity; i 
magnitude only, and no direction 
The pressure exerted by a gas against the walls of its container will always be perpendicular(normal) to the container walls
Essential Equations: Fluids