APPLIED MECHANICS THERMODYNAMICS
CHAPTER 1
3 fundamentals of fluid mechanics
UNITS ‼
Bernoulli's equation
energy equation (see above for definition
linear momentum equation = Newton's second law for fluid streams
conservation of kinetic, potential, and pressure energies of a fluid stream
their conversion during idealized frictionless flow
fluid mechanics = mechanical energy // thermal energy 🚩
their conversion via friction loss // mechanical energy loss = conversion of mechanical energy into thermal energy
enery equation = conservation of mechanical energy
determine the force caused by fluid flows
- mechanical energies and efficiency of mechanical work devices
(pumps and turbines) - head loss
Reynolds transport theorem
Fluid systems = transport a fluid from one location to another with
- a specific rate
- velocity
- elevation
In general, this system = mechanical energy + frictional effects.
Because
A system can generate or consume mechanical work, such as turbine or pumps, fans, respectively.
NO conversion of nuclear, chemical, or thermal energies into mechanical energy.
NO heat transfer
BUT with constant temperature.
reversible turbine coverts pressure energy P/rho into mechanical energy
.
Meaning
NOTE: thermal energy is not included into the mechanical energy
mechanical energy = KE + PE + Pr E ❤
Mechanical energy = Kinetic energy + Potential energy + Pressure energy.
mechanical energy is entropy free
Presure energy Pr E = P.v = P/rho = g.h
- energy per unit volume (J/m3)
- or energy per unit mass (J/kg)
J/m3 = J/kg = N/m2 = Pa ❤ - (related to gage pressure) vs. flow energy (related to absolute pressure) ❗
mechanical work = shaft work
shaft work in turbines, pumps, fans
mechanical efficiency of a device/process
❤
pump efficiency: by supplying mechanical energy to the fluid by the pump (fan, compressor)
❤
turbine efficiency: by extracting mechanical energy from a fluid
where
= the rate of decrease in the mechanical energy of the fluid ❤
W' pump, u: useful pumping power supplied to the fluid
AND
: the increase in mechanical energy of the fluid ❤
Generator efficiency (a hydraulic turbine is usually packed with its generator)
Motor efficiency (a pump is usually packed with its motor)
DEFINITION: is a relation b/w pressure, velocity, and elevation in steady, incompressible, frictionless flow. [in other words, for the idealized flow the fluid motion is governed by the combined effects of pressure and gravity forces].
- NOTE: with assumption that neglects the vicous effect (~ in the frictionless flow) and surface tension.
motion of a particle
Newton's second law
a = Fnet / m
OR
Fnet = m • a (1 Newton = 1 kg • m/s2)
combined/overall efficiency of pumps and turbines
EXAMPLE
Pr E = Wmax, turbine ❤
- reference level = datum: at the bottom
- h: height filled with water = the vertical distance of the point from the free surface.
- At point A, gage pressure: P A = 0, and potential energy per unit mass: p eA= g.h
- at point B, gage pressure P B = rho.g.h and p eB=0
For a perfect hydraulic turbine,
the work w turbine at point A = w turbine at point B = g.h (J/m3) or = P.v = P/rho (kJ/kg)
Note that: at point A, w turbine = potential energy
At point B, w turnbine = pressure energy
For a stationary fluid with constand density
SUM pressure energy and potential enery = constant ❗
Bernoulli's equation
Bernoulli's equation
limitation of the use of Bernoulli's equation ❤
- when the frictional effects cannot be neglible.
EXERCISE SESSION 2
WORD FILE
FORMULARIUM_LAB SESSION
FORMULARIUM _LECTURE SESSIONS