Fluids Flashcards
True or false:
The behavior of an object in a fluid is determined by the relationship of the densities of the object and the fluid.
True
Standard pressure is?
1 atm = 760 mmHg = 760 torr
Motion/free-body diagram of an object in a fluid moving down
Viscosity
The measure of a fluid’s resistance to flow
SI unit: Pa*s
Specific gravity
It is used to determine if an object will sink or float in water.
Calculating specific gravity
Specific gravity =
density of object or fluid /density of water
If an object has a specific gravity of exactly 1, what does that mean?
If an object has a specific gravity of .92, how much of it is submerged?
The object will be fully submerged in water, but it will not sink.
92% of the object is submerged, while 8% is not.
Density
p = m/v
SI unit: kg/m^3
other units: g/mL or g/cm^3
density of water
1 g/cm^3 or 1000 kg/m^3 or 1 kg/L
Equation relating density to volume of fluid and object
Vfluid is the volume of fluid displaced or the volume of the object submerged
Vobject is the total volume of the object itself.
You can use this to find the density of an object knowing only the percentage of the object submerged.
How do you find the density of an object in a fluid, when given the # of the fraction of the object floating and the density of the fluid.
Density of object = density of fluid x fraction proportion of object submerged
*Make sure if given the fraction of object floating to subtract from 1, to get the fraction submerged
Calculating fraction an object submerged
Fraction submerged = density of object/density of fluid
Pressure equation
P = Normal Force/Area
SI unit: Pascal
Other units: 1 N/m^2 = 1.013 x 10^5 Pa = 760 mmHg = 760 torr = 1 atm
What is absolute pressure?
The total pressure exerted on an object that is submerged in a fluid
Calculating absolute pressure
P = P0 + pgz
P0 is pressure at the surface. Usually 1 atm.
z is the depth the object is being submerged
How does depth affect the absolute pressure?
The deeper an object is, the higher the absolute pressure.
Gauge pressure
P (absolute pressure of the object) - Patm (atmospheric pressure)
Calculating hydrostatic pressure (the pressure exerted by the weight of the fluid above a point)
density of fluid gh
h is the depth the object is at
How to calculate weight force of object in fluid when given density
weight force of an object = density of object x volume of object x g
Liquids are (compressible/incompressible) fluids while gases are (compressible/incompressible) fluids.
Incompressible, compressible
Pascal’s Principle Equations
P1 = P2 = F1/A1 = F2/A2
V1 = V2 = A1d1 = A2d2
What does Pascal’s Law state?
It states that pressure applied to a ideal fluid is uniformly transmitted to all regions of the fluid. Pressure is constant.
Important things to know about a Hydraulic Lift setup:
-Amt of liquid(volume) displaced on left = amt of liquid(volume) displaced on right
-One side has a larger distance/smaller area and other side has a smaller distance/larger area
-Larger cross-sectional area has a greater force
-Pressure throughout the whole system is the same
-The work remains the same throughout
Archimedes principle
An object partially/fully immersed in a fluid will be buoyed upwards by a force equal to the weight of the fluid that is displaces.
Key ASPECT of Archimedes principle
When an object is placed in a fluid, the volume of the displaced fluid is equal to the volume of the object.
Define buoyant force
It is the force that a fluid exerts upward on an object which is submerged in the fluid.
When given the weight of a person outside of water and the weight of a person submerged in water, how do you calculate buoyant force (Fb)?
Fb = Weight in the air - Weight submerged in water
Calculate bouyant force.
Fbuoy = density of fluid * volume of fluid displaced * g
g is 10 m/s^2
True or false:
Objects of different masses which displace the same volume of fluid, will experience the same magnitude of buoyant force.
True, buoyant force isn’t dependent on the object’s mass. Only the mass of the fluid itself.
True or false:
IF an object is floating (even if it’s 98% submerged), the buoyant force = weight of the object.
True; Fb = Fw or Fb = mg
buoyant force = gravitational force
Adhesion vs. cohesion
Adhesion - attractive force that liquid molecules feel towards other substance’s molecules (can be a solid)
Cohesion - attractive force a molecule of liquid feels toward another one of its own molecules
Surface tension definition & formula
The tension of the surface film at the top of a liquid due to the attraction of the particles & tendency to minimize surface area
F (Surface tension) = 2γL
*L is the the circumference (2πr or πd)
*γ is a given constant
Poiseuille’s Law
Calculates the laminar flow rate of a viscous fluid
-Radius of tube^4 is directly proportional to flow rate
-Pressure difference is directly proportional to flow rate
-Pressure difference and radius of tube are indirectly proportional to each meaning if radius of tube decreases by 1, the pressure would increase x4 (explains why blocked vessels have such high pressure)
Define linear speed of a fluid
The linear displacement of fluid particles in a given amount of time.
Define volumetric flow rate and how to calculate it?
The volume of fluid that passes in a tube per unit time.
Q = v*A
v is linear speed/velocity, A is cross-sectional area
Area for a tube: π *r^2
Calculating mass flow rate:
Mass flow rate = Avfluid density
In a closed system, flow rate is ________, while linear speed changes relative to ________.
Constant; cross-sectional area
True or false:
Fluids flow more quickly through narrow passages and more slowly through wider passages.
True
Relationship between the radius of a tube and pressure
Inversely proportional to the 4th power.
Define laminar flow
The flow of a fluid which is smooth and orderly, parallel lines on diagrams
Define turbulent flow
Flow of a fluid that is disorderly and characterized by swirls called “eddies”
How can turbulent flow of a fluid occur?
When the speed of a fluid exceeds a certain critical speed (could be due to a small radius of the tube), turbulent flow can occur.
Turbulent flow of a fluid in a cup, can be caused by stirring the fluid. When the stirring stops, why does the turbulent flow gradually stop?
The energy put into the flow by stirring is dissipated by the fluid’s viscosity.
Once the stirring stops, the only force acting on the flow is the viscous shearing force resulting from the velocity gradients present within the fluid. Consequently, the kinetic energy is dissipated by frictional shearing forces such that the velocity decreases dramatically.
Compare ideal fluids vs. non-ideal fluids
Ideal - no viscosity, laminar flow, incompressible (water & mercury)
Non-ideal - have viscosity, turbulent flow, compressible
Continuity equation
A1V1 = A2V2
A is area and v is speed/velocity
Trick question: how changing the area affects velocity
-Applying the continuity equation, area and velocity are inversely proportional
-The trick is the question says the diameter is reduced x2, HOWEVER when calculating the area of a blood vessel we use radius (r^2)
-Therefore, the diameter reducing x2, is the same as the radius reducing x4
-As radius is reduced by 4 –> area reduces by 4 –> velocity increases x4
Bernoulli’s equation
Key aspects of Bernoulli’s equation
-Describes the conversion of energy in ideal fluids between two points in a conduit
-Velocity and pressure are inversely related
-As velocity increases, pressure decreases in an ideal fluid
-Venturi EFFECT: as tube diameter decreases, the velocity increases/pressure decreases
Simple fluid barometer diagram
*In this setup atmospheric pressure is equal to hydrostatic pressure (pgh)
Venturi Effect
Says that the pressure of an ideal fluid in motion will decrease as fluid velocity increases
How does high blood pressure affect cardiac output, stress, and blood velocity?
High BP causes increased cardiac output, increased blood velocity, and increased stress on the arteries.
Hard question, key takeaway
A downward force was applied, causing the net force to increase from 0, object starts to sink down.
Once this force is removed, the object’s net force goes back to zero HOWEVER, the object still sinks w/ a constant velocity. Newton’s 1st Law says an object in motion will stay in motion.
Bernoulli equation question: Height is proportional to what aspect in the bernoulli equation?
h is directly proportional to Pa - Pb as well as to (velocityb)^2
If an object has sunk to the bottom, what is the relationship between buoyant force and gravitational force?
Buoyant force < gravitational force (weight of object)
True or false:
For the same object, when immersed in different fluids, the greater the specific gravity (density) of the fluid, the bigger the buoyant force.
When the object is fully submerged in each fluid, the volume of fluid displaced = volume of the object, THUS the volume of the fluid displaced is CONSTANT no matter the type of fluid used.
True,
IMPORTANT CONVERSION
1 mL of water = 1 g of water
1 L of water = 1 kg or 1000 g of water
When to use Pousille’s law vs continuity equation?
Pousille’s - Used in problems where flow rate is not constant, applied to non ideal fluids (viscous fluids)
Continuity - Applied to constant flow rate systems
