APPLIED MECHANICS THERMODYNAMICS
CHAPTER 1

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3 fundamentals of fluid mechanics

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UNITS ‼

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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
Screenshot 2018-11-18 15.23.55
Screenshot 2018-11-18 15.24.00 .
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
Screenshot 2018-11-18 17.01.40
Screenshot 2018-11-18 17.02.29

pump efficiency: by supplying mechanical energy to the fluid by the pump (fan, compressor)
Screenshot 2018-11-18 17.08.14
Screenshot 2018-11-18 17.09.12

turbine efficiency: by extracting mechanical energy from a fluid
Screenshot 2018-11-18 22.03.20
Screenshot 2018-11-18 22.03.25
where
Screenshot 2018-11-18 22.04.22 = the rate of decrease in the mechanical energy of the fluid

W' pump, u: useful pumping power supplied to the fluid
AND
Screenshot 2018-11-26 15.45.16 : the increase in mechanical energy of the fluid ❤

Generator efficiency (a hydraulic turbine is usually packed with its generator)
Screenshot 2018-11-18 22.09.38
Screenshot 2018-11-18 22.09.41

Motor efficiency (a pump is usually packed with its motor)
Screenshot 2018-11-18 22.07.48
Screenshot 2018-11-18 22.08.09

Screenshot 2018-11-18 22.14.31 Screenshot 2018-11-18 22.14.37

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.
    Screenshot 2018-11-18 22.29.39

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 ❤

Screenshot 2018-11-18 15.49.02

  • 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

Screenshot 2018-11-18 22.12.40 Screenshot 2018-11-18 22.12.45

Bernoulli's equation
Screenshot 2018-11-27 22.08.43

Bernoulli's equation
Screenshot 2018-11-27 22.09.29

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