fluids Flashcards
define the states of matter
solid - definite shape and volume
liquid - takes shape of container, but has definite volume
gas - takes shame and volume of contianer
special states:
plasma
bose-einstein condensate
define density
represented by Greek letter “rho”
rho = p
kilograms per cubic meer
define FLUID
material takes that shape of its container and yields easily to external pressures (gases and liquids are fluid)
are liquids compressible
generally no, that’s why hydraulics work, and generally the work is defined as…
pressure
P = Force/area
N / m^2
N / m^2 is known as a pascal
how does pressure change as we go deeper in a fluid
increases LINEARLY, P = P0 + pgh (small p intentional)
guage pressure
delta P = pgh, change does not take into account that initial P0 bcz its change
what is change in pressure also known as?
gauge pressure, difference in initial and absolute pressure, a measuring device will probably tell you the gauge pressure, not absolute pressure
when an object is submerged in water, pressure is (greater/less than/equal to) at the top of the object and (greater/less than/equal to) at the botton of the object
less at the top, greater at the bottom, as the deeper you go the higher the pressure
what is the pressure of an object in a fluid when the fluid is at rest?
hydrostatic pressure
pressure depends on (depth, total amount of water in container, shape of container)
assuming the atmospheric pressure is the same, depth only! (even if the surface is not directly aligned with the point of pressure, such as a winding cave going very far to the left)
absolute pressure
P = P0 + pgh (where small p = density)
define pascal’s law
pressure applied to a fluid, when the fluid is contained everywhere else, is applied by that same fluid in every other direction with equal force over equal areas
given a cube with a 1 inch^2 opening, with 10 lbs of force applied to a stopper within the opening, what is the total resulting force acting on the bottom of the container? (the bottom has an area of 20 in^2)
200 lbs
in a closed system, the (pressure/force) is the same everywhere
PRESSURE, the FORCE depends on the surface areas of different parts of the system
archimedes’ principle
the buoyant force of an object is equal to the WEIGHT (force of the MASS, N O T volume) of the fluid displaced
Fb = pVg
define buoyancy
the upward force of an object within a fluid/net force from fluids surrounding an object
(true/false) buoyant force is dependent on object depth
false, as we are assuming that ideal fluids are incompressible and thus density does not change
why is the pressure the same at the same height despite different amounts of water?
greater total force at that z depth plane, yes, but more spread out
in what direction does pressure act?
all directions, with all normal forces perpendicular to the walls
RMR: CONSERVATION OF FORCE IS NOT A THING
that’s why pascals law works!
pressure equation
P = Force/area
what is conserved in a hydraulic system?
work!
work = force * distance,
as you increase force due to pressure it moves less distance up on the heavier side
archimedes’ principle
object is buoyed up by force = to the WEIGHT of the fluid displaced
weight of fluid with same volume
buoyant force takes into account the….
FLUID, Fb = density * volume * gravity
density and volume are OF THE FLUIDDDDDDDDDDDDDDDd
an iceberg with an average density of 910 kg/m^3 and a mass of 52,000 kg floats in sea water with a density of 1030 kg/m^3
a. What is the buoyant force acting on the iceberg?
b. What percentage of the iceberg is submerged beneath the water?
a. its FLOATING! thus net force is zero, thus
52,000 * gravity = 510,120 N = FB
b. solve for TOTAL volume, 52,000/910, = 57.1 m^3
Buoyant force = the weight of water displaced —-> we can find the water displaced!
510,120 N = pv * g
510,120 /(9.81 * 1030) = v
v = 50.5 m^3 of water displaced, thus 50.5 m^3 of iceberg covered!
50.5/57.1 * 100 = 88.44%!!!!!
continuity equation (fluid moving through a pipe)
A1v1 = A2v2
same amount of fluid, given a larger area input a smaller area output must have a larger velocity of output
1 kg/second = 1 kg/second, CONSERVATION OF MASS IN A FLOW
mass flow rate
in a fluid with an area of high pressure and an area of low pressure, the high pressure will flow into the low pressure area
this is doing force, kind of like a transfer of energy
thus along came bernoulli
Bernoulli’s principle
higher velocity =lower pressure in a fluid flow
how does a spinning ball curve?
ball is spinning, on one side spinning with the air, thus speed of air relative to surface of ball is different on front and back side, thus motion
how does a ball float on a leafblower’s stream of air even when moved from side to side?
because the leaf blower creates a low pressure system by increasing speed, thus the surrounding air has higher pressure and keeps it in the “column”
describe the same fluid moving through different sized areas via the continuity equation
LARGER area = slower, lower pressure
SMALLER area = faster, higher pressure
Bernoulli’s equation
pressure + 1/2 * density * velocity^2 + density * gravity * initial height = pressure(2) + 1/2 * density * velocity^2 + density * gravity * height
P1 + 1/2pv0^2 + pgy = P2 + 1/2pv^2 + pgy
basically conservation of energy, at one location given the same flow it will be the same at another location
(effectively adding pressure, “kinetic energy,” and “potential energy”)
water circulates thru a house in a hot-water heating system. if the water ris pumped at a speed of 0.5 m/s through a 8.0 cm diameter pipe in the basement under a pressure epf 3.0 atmp, what will be the flow speed and pressure in a 5.2 cm diameter pipe on the second floor 5.0 meters above?
2.5 x 10^5
bernoulli’s equation + continuity equation
pressure decrease makes sense conceptually because the area is smaller so it goes faster, as well as the height beneath the water decreasing thus the pressure also decreases
we know that at the opening pressure is atmospheric pressure because, well, its an opening, so P2 = 1.0 x 10^5, and we can use bernoulli’s equation to set it up because its still technically part of the system
we can use Bernoulli’s equation to set up this:
200000 + 1.210002^2 + 0 = 100000 + 1/21000v^2 + 1000*9.8 * 0.7
v = 13.8 m/s
plug it into the conservation of energy or kinematic equation:
1/2mv^2 = mgh
1/2(13.8)^2 = (9.81)h
h = 9.7 meters!!!
large soda bottle with a hole in the side
when area of fluid at the beginning area is substantially larger to make its velocity neglible compared to the tiny output:
gh = 1/2v^2
