Lecture 1 Flashcards
Basic concepts of mechanics, Hydrostatics. Hydrodynamics. Motion of ideal fluids. Motion of real fluids. Viscosity. Laminar and turbulent motion. Blood pressure measurement.
What is a fluid
A fluid is a substance that can flow
What is fluid statics/hydrostatics
The branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium
What is fluid dynamics
Deals with fluid flow; the science of liquids and gases in motion
What are normal stress forces
When a body is immersed in a fluid
What is pressure numerically equal to
The normal force acting per unit area of the surface
Equation including pressure, normal force and surface
p=Fn/S
Units for the equation including pressure,normal force and surface
[p]=N/m^2=Pa
-The SI unit is Pascal [Pa] and is defined as one newton per square metre(N/m^2)
-Atmospheric pressure is measured in hectopascals (hPa); 1 hPa=100Pa
Millimeter of mercury for the pressure
1mmHg= 0.0013158 atm= 133.322 Pa
1 bar= 10^5 Pa
What are SI units
The International System of Units (SI), known as the metric system, is the international standard for measurement
What are the 7 SI base units
Length- metre (m)
Time- second (s)
Amount of substance- mole (mol)
Electric current- ampere (A)
Temperature- kelvin (K)
Luminous intensity- candela (cd)
Mass- kilogram (kg)
Pascal’s law
States a change in the pressure applied to a fluid is transmitted undiminished (equally) to every point of the fluid and to the walls of the container.
What does the pressure in a fluid depend on
It depends on the depth and the value of po. An increase in pressure at the surface at the surface must be transmitted to every other point in the fluid.
p=constant for all points of the fluid
Pressure created by liquid and gases
Liquids and gases create pressure in all directions. The pressure at any point of a stationary fluid is the same
Fluid pressure formula
p=F/S
pressure is a scalar quantity
Hydraulic press in Pascal’s law
This is an important application of Pascal’s law. The volume of liquid pushed down on the left must equal the volume pushed up on the right
Hydrostatic pressure
The pressure exerted by a vertical column of liquid (or gas) of cross-section S and height h on the base of the column depends on its weight and the pressure is:
p=pgh
What does the hydrostatic pressure depend on
It is greatest at the bottom of the vessel and is 0 at the free surface of the fluid.
It does not depend on the shape of the vessel, but only on the height of the liquid above the given location.
Archimedes’ law
The magnitude of the buoyant force FA always equals the weight of the fluid displaced by the object. This law is the basis for the floating of bodies
Equation for Archimedes’ law
FA= pgv
Ideal fluid
It is a fluid in which the internal friction between its layers is neglected and it is treated as incompressible.
Mach’s number
Mach’s number is the criterion for the compressibility of gas media;
M=v/vs
Units for Mach’s number
v- velocity of the gas flow
vs- velocity of sound in the gas flow
The 2 methods in hydrodynamics for studying the fluid motion
Lagrange method (statistics)
Euler’s method
Euler’s method
Examines the distribution of the velocity vector for the space occupied by a fluid
Velocity vector field
The set of velocity vectors for all points in the fluid
It can be graphically depicted using fluid lines and fluid pipes
Steady-state assumption
If the velocity at any point in the fluid does not change with time, the motion of the fluid is stationary.
Continuity for an incompressible fluid
The volume of fluid that passes any section of the tube per second is unchanged. The fluid that enters one end of a pipe or an artery at the flow rate, must leave the other end at a rate which is the same.
Equation of continuity
S1xV1 = S2xV2
What is Bernoulli’s equation
States that the pressure plus the total mechanical energy per unit volume is constant everywhere in the fluid.
Conditions for Bernoulli’s equation
1) The fluid is incompressible, then the density remains constant
2) The fluid is non-viscous (no mechanical energy is lost)
3) The flow is streamlined, not turbulent
4) The velocity of the fluid at any point does not change during the period of observation
Bernoulli’s equation
p+1/2pv1^2 + pgy = constant
or between two sections
pv1^2/2 + pgh1 + p1 = pv2^2/2 + pgh2 + p2
dynamic, hydrostatic and static pressure (p)
Bernoulli’s equation for a horizontal tube
pv^2/2 + p = constant
When can Bernoulli’s equation not be used
It occurs when real fluids in motion exhibit some effects of frictional or viscous forces. Whenever the work done against these dissipative forces is comparable to the total work done on the fluid or its mechanical energy Bernoulli’s equation cannot be used
Motion of real fluids
Because of viscosity when real fluid is forced through a tube, it flows more quickly near the tube’s axis than near its walls.
In general, viscosity depends on the fluid’s state such as its temperature, pressure and rate of deformation
Newton’s law of viscosity
In the laminar movement of real fluids, tangential forces of internal friction act between adjacent layers
Newton’s law of viscosity formula
F=n[du/dy]S
The two modes of fluid motion
Laminar and turbulent
Laminar motion
It is a slow motion in which the trajectories of adjacent fluid particles differ little from each other
Turbulent
Occurs with a gradual narrowing of the cross-sectional dimensions of the tube or an increase in the flow rate, intensive mixing of the liquid occurs and the laminar regime passes into turbulent
Methods for measuring the viscosity
Stokes method
Poiseuille method
Stokes method
-In case n> 0.1 Pa.s stokes method is applied
-Consists of measuring the parameters of the movement of small spherical bodies during their uniform fall into a viscous fluid.
Poiseuille method
For fluids with a lower viscosity, this method is applied and is based on the laminar movement of the fluid in a thin capillary.
The relation between viscosity and temperature
-As the temperature increases, viscosity decreases for liquids
-As the temperature increases, viscosity increases for gases
-Because viscous forces are usually small, fluids are often used as lubricants to reduce friction
Pressure measurements
Barometer
Manometer
Barometer
-A long-closed tube is filled with mercury and inverted in a dish of mercury
-The closed end is nearly a vacuum
-Measures atmospheric pressure as Po=phg g h
-One 1atm = 0.760 m (of Hg)
Manometer
-A device for measuring the pressure of gas contained in a vessel
-One end of the U-shaped tube is open to the atmosphere
-The other end is connected to the pressure to be measured
Blood pressure- Sphygmomanometer
It is used in the upper arm where it gives values nearly close to the pressure in the heart.
Also, the upper arm contains a single bone making the brachial artery located there easy to compress
Systolic pressure
The heart exerts pressure on the blood in the circulatory system only during the contraction of the left ventricle
Diastolic pressure
When arteries contract they expand, and during the pauses between them they contract and exert pressure on the blood
Blood velocity
It is greatest in the aorta (about 50 cm/s^-1) and gradually decreases in arteries, arterioles and capillaries to approximately 0.5 mm/s^-1
Pulse wave speed
Determined by the elasticity of the blood vessels. Its normal values are between 6 and 8 m/s^-1
Blood pressure
Blood pressure in medicine is called the difference between the pressure of the blood in a certain blood vessel and the atmospheric pressure
Cannula
A small glass or plastic tube containing saline solution plus an anti-clotting agent.
