Fluids Flashcards
density
p = m/v
density of water
1 g/cm^3 = 1 g/mL = 1000kg/m^3
weight of object using density
Fg = pvg
density x volume x gravity
specific gravity
density of new object/ density of water = specific gravity of new object
pressure
P = F/A
measured in Pa
Pascal
Pa
Kg/m s^2
Pascal to torr
1.013 x 10^5 Pa = 760 torr
Pascal to mmHg
1.013 x 10^5 Pa = 760 mmHg
Pascal to atm
1.013 x 10^5 Pa = 1 atm
absolute hydrostatic pressure
total pressure exerted on an object that is submerged in a fluid
think of diving into pool. Pressure is the surface plus everything underneath
P = P0 + pgz
absolute pressure = surface pressure + density x gravity x depth of object
gauge pressure
pressure relative to atmospheric pressure. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below
Pgauge = P - Patm
Equation when P0 = Patm
when surface pressure = atmospheric pressure
Pgauge = pgz
hydrostatics
study of fluids at rest and forces and pressures associated with standing fluids
Pascal’s principle
fluids that are incompressible when a pressure is exerted onto them will evenly distribute the pressure throughout the system which causes pressure to be dealt with elsewhere
ex: press on milk can and the cap will pop off because the pressure needs to go somewhere and the fluid can’t be compressed
Pascal’s Principle equation
P = F1/A1 = F2/A2
F2 = F1 [A2/A1]
volume equation for hydrostatics
V= A1d1 = A2d2
d2 = d1[A1/A2]
the larger the area, what is the force and distance
larger the area, larger the force, over a shorter distance
smaller area, smaller force, over a larger distance
Archimedes Principle
mass of fluid displaced exerts a force equal to its weight against the submerged object
Fbuoy=p(fluid)V(fluid displaced)g = p(fluid)V(submerged)g
object will sink until volume of displaced volume exerts a force that is equal to the weight of the object
how far it sinks depends on how dense it is
buoyancy and specific gravity
the object’s specific gravity as a percentage indicates the percentage of the object’s volume that is submerged
ex: 0.92 g/cm^3 = 92% submerged = 8% sitting above surface
object with specific gravity less than or equal to one
will float in water
specific gravity of exactly 1 indicates
the object is 100% submerged but will not sink
adhesion
attractive force that a molecule of a liquid feels toward molecules of a different liquid
cohesion
attractive force that a molecule of a liquid feels toward molecules of the same liquid
fluid dynamics
study of fluids in motion
viscosity
how easily fluids flow
n = resistance of fluid to low
increased viscosity will increase viscous drag –> nonconservative force
acts opposite of flow
laminar flow
smooth and orderly
layers of fluid that flow parallel to one another
Poiseuille’s Law
rate of flow in a laminar flow
Q = πr^4ΔP/8ηL
or
Q = ΔP/R
R= 8ηL/πr^4
Q=volume flowing/time (m^3/s)
η=viscosity
ΔP=pressure gradient (Pa)
relationship between radius and pressure gradient
radius to the fourth power is inversely proportional to the pressure gradient
r^4 ∝ 1/ΔP
calculating critical speed
Vc=Nη/pD
Vc = critical speed N = constant: Reynolds number (depends on size, shape, and surface roughness) p = density D = diameter
flow rate
volume/unit time
linear speed
measure of displacement of a fluid in a given amount of time
Continuity equation
Q = A1V1 = A2V2
fluids flow more quickly through narrow passages and more slowly in wider ones
Bernoulli’s equation
static pressure + dynamic pressure = total pressure
P + 1/2pv^2 + pgh = P + 1/2pv^2 + pgh
P= absolute pressure of the fluid p= density of the fluid v= linear speed g= acceleration due to gravity h= height of the fluid above some point
dynamic pressure equation
1/2pv^2
pressure associated with movement of a fluid
essential the kinetic energy of fluid / volume
p=m/v
static pressure
P + pgh
same as the equation for absolute pressure
venturi flow meter
as tube narrows, speed increases
the dynamic pressure will increase but absolute pressure will decrease when the tube narrows, resulting in the smallest height for water in the tube at the narrowest areas
circulatory system in relation to blood flow
closed loop
non-constant flow rate
total resistance decreases because of the number of vessels in parallel
blood flow return to heart is facilitated by
mechanical squeezing of skeletal muscles
increases pressure in limbs increases blood to heart
as we breath in
volume of lungs increases so pressure decreases so air flows down concentration gradient
Speed of blood in aorta is faster than in a capillary bed because?
the cross sectional area of capillary bed is larger so it will flow slower
each blood vessel divides into thousands of little capillaries
hydrostatic pressure
pressure at the bottom of the cylinder
pressure exerted by the weight of a fluid
ΔP = pgh (density x gravity x height)
would a larger or smaller object have a greater buoyant force?
the larger object has a greater buoyant force because it will displace more volume
how should speed of water be changed to increase pressure and force?
decrease speed to increase pressure and force
the venturi effect
when something moves quick, it has ___ pressure
lower pressure
when something moves slower, it has ___ pressure
higher pressure
vernuli’s equation
units for flow rate (Q)
m^3/s
units for ΔP
Pa = N/m^2 = Kg/m*s^2
ohm’s law of flow
ΔP = Q x R
therefore pressure is directly proportional to both flow rate and resistance
the blood vessels with the greatest pressure drop would have the most peripheral resistance
What vessel has the highest peripheral resistance?
arterioles because they have the largest pressure drop
they act as the main regulatory of BP and are very muscular and significantly change vessel radii
what causes the pressure fluxuations in the arteries?
systolic vs diastolic
the heart will either contract or expand which affects the pressure in the arteries as blood is pumped through the systemic portal to the body
Why don’t capillaries have the highest peripheral resistance?
While capillaries have the smallest vessel radii and have the highest individual resistance, the sheer number of them in parallel will decrease the equivalent resistance
