Fluid: system that yield to any force that attempts to alter their shape, causing system to flow until it reaches mechanical equilibrium; fluid conforms to shape of container
Can We Help with Your Assignment?
Let us do your homework! Professional writers in all subject areas are available and will meet your assignment deadline. Free proofreading and copy-editing included.
Molecules of liquid in condense state; maintain CONSTANT intermolecular distance. Liquid will form SURFACE. Gas will not form surface; adjust intermolecular distance to fill space provided (compression/ expansion)
Fluid in mechanical equilibrium; fluid= stationary
Equilibrium: state in which all essential parameter of system are TIME-INDEPENDENT; no observable change while you observe system
Ideal Stationary Fluid:
- Incompressible; volume & density remain constant (applies for liquids and IDEAL gases, not real gases)
- Deformable; under the influence of forces and
- Seeks a mechanical equilibrium
- Once mechanical equilibrium is reached; fluid= stationary (apples to both liquids & gases)
Consequence: Density= CONSTANT
- Pressure of ideal fluid varies with vertical distance
- Take a fluid block, tiny, able to locate, define as (bottom: y1 top: y1 + dY) (Fnet,y= 0= Fup-(W+Fdown)
The difference between the pressures at two different positions in a fluid is proportional to the vertical distance between these two positions. The proportionality factor is the produce of the density of the fluid and the gravitational acceleration
|W|= g x dn= density x gravity x Area x dY
- P2-P1= -density x gravity (Y2-Y1) * General Form (pressure change is linearly proportional to change in Y value) used when the surface of the fluid can’t be identified for a reference point (i.e blood in veins) as you go down (increase Y, you will increase P)
- P (ymax)=0= Patm + density x gravity x depth (in atm)*Used when surface is found; express it as pressure at surface + weight of water column above depth (identify surface of fluid toward ambient atmosphere or a vacuum due to mechanical equilibrium between air pushing down on water and water pushing up
- Convert Density into kg/m^3. ON EARTH!
- Pascal Law doesn’t apply to fluid air (can’t explain pressure variation in atmosphere)
- Atmosphere is NOT a stationary fluid because density is NOT constant
- Doesn’t apply to gases because gases are compressible and their density depends on pressure.
- Pascal’s law doesn’t explain shape of container; Pressure increases below surface to given fixed value at any given depth; regardless of container shape.
P1 = P2 (since the pressures are equal throughout).
F1/A1 = F2/A2 ——– P=F/A
V1 = V2 (fluid pushed down on the left side equals the volume of fluid that is lifted up on the right side, the following formula is also true.)
- Blood pressure is a gauge pressure (unlike absolute pressure, gauge pressure can be -/+) (pblood= pabsolute – patm) (pressure relative to air pressure that varies throughout the cardiovascular system
- If we had negative gauge pressure in blood vessel, it would collapse; though values are below (0), pressure in blood is not below 1 atm (negative gauge pressure, a way of expressing pressure measurements below atmospheric pressure)
- For measurements in blood use general formula: P2-P1= density x gravity (Y2-Y1)
∆p= densityblood x g x ∆y (if (-) it means the change from the heart to the brain. So heart pressure- (calculated pressure) = pressure in brain
∆p= pressure change from heart to brain
∆y based on vertically y-axis pointing upward
In blood the pressure at the heart becomes the atmospheric pressure [gauge= abs = heart pressure]
- High: found in aorta, arteries, arterioles, capillaries
- Diastolic (80mmHg (10.7kpa) – Systolic (120mmHg (16.0kpa)
- Low: veins, pulmonary circulation
- Cardiovascular system will exceed ambient air pressure everywhere ONLY WHEN LYING DOWN
- Taller animals will have higher systolic blood pressure in order to compensate for having to pump blood farther around the body
Buoyancy (Archimedes Principle)
- Buoyancy: an upward acting force exerted by a fluid, which opposes an object’s weight. (Buoyancy = weight of displaced fluid.)
- If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat.
- Archimedes’ principle does not consider the surface tension (capillarity) acting on the body.
- When at mechanical equilibrium (Fup-Fdown-Wf= 0)
- However the (Fup-Fdown= Wf > 0)
- Fnet>0= weight of block is less than weight of displaced fluid, air bubbles (block B) rises to the top
- Fnet=0 Block will float at its current depth
- Fnet<0 weight of block is greater than the weight of the displaced fluid and the block will sink to the bottom of the container.
- Archimedes principle: When an object is immersed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid displaced by the object.
Pbuoyant= Densityfluid x Volumeobject x gravity (replaced Wf not Fnet)
- Buoyant force is ALWAYS directed upward (opposite of gravity) (as volume increase, buoyant forces increase) **if all other parameters are kept equal
- Whether something floats or sinks is NOT determined by weight but by its density/ volume relative to the density of the surrounding fluid.
- Having salt water can vary the density of the liquid as compared to fresh water. The weight of the water INCREASES as the salt content increases.
- ‘Buoyancy force in air = weight of object in empty space – weight of object immersed in fluid’
Suppose a rock’s weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons.