**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

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**

## Pascal’s Law

- Pressure of
**ideal**fluid varies with vertical distance - Take a fluid block, tiny, able to locate, define as (bottom: y1 top: y1 + dY)
*(F*_{net,y= }0= F_{up}-(W+F_{down})

*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*

* *

*P*_{2}-P_{1}= -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= P**(in atm)_{atm}+ density x gravity x depth**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

- Blood pressure is a
**gauge pressure (unlike absolute pressure, gauge pressure can be -/+) (p**(pressure relative to air pressure that varies throughout the cardiovascular system_{blood}= p_{absolute }– p_{atm}) - 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:
*P*_{2}-P_{1}= density x gravity (Y2-Y1)

∆p= density_{blood} 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 (F
_{up}-F_{down}-W_{f}= 0) - However the (F
_{up}-F_{down}= W_{f }> 0) - F
_{net}>0= weight of block is less than weight of displaced fluid, air bubbles (block B) rises to the top - F
_{net}=0 Block will float at its current depth - F
_{net}<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.

**P _{buoyant}**= Density

_{fluid}x Volume

_{object}x gravity (replaced

**W**not

_{f}**F**)

_{net}**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.*

*SchoolWorkHelper*, 2019, https://schoolworkhelper.net/pascals-law-buoyancy/.

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