# NON FLOW AND FLOW WORK

** NON FLOW AND FLOW WORK **

**CLASS NOTES FOR MECHANICAL **

**ENGINEERING**

NON FLOW WORK

NON FLOW WORK

**(i) ****Work input to a compressor during compression process ( from the start of compression to end of compression)**

**(ii) ****Work obtained from a turbine during expansion only (During start of expansion to the end of expansion)**

**Mathematical form of non-flow work = area under the curve= w =∫pdv= (p**_{2}v_{2} — p_{1}v_{1})/(γ – 1) kJ/kg

_{2}v

_{2}— p

_{1}v

_{1})/(γ – 1) kJ/kg

**w= work input kj/kg**

**v**_{1} = specific volume at point 1

_{1}= specific volume at point 1

**v**_{2} = specific volume at point 2

_{2}= specific volume at point 2

** Total energy entering a system=Internal energy + Flow energy + Kinetic energy +Potential energy + heat supplied= m**_{i }(u_{i} +P_{i}v_{i} +C_{i}^{2}/2 + gz_{i})+Q

_{i }(u

_{i}+P

_{i}v

_{i}+C

_{i}

^{2}/2 + gz

_{i})+Q

**Total energy leaving a system=Internal energy + Flow energy + Kinetic energy +Potential energy + Work obtained= m**_{i }(u_{0} +P_{0}v_{0} +C_{0}^{2}/2 + gz_{0})+W

_{i }(u

_{0}+P

_{0}v

_{0}+C

_{0}

^{2}/2 + gz

_{0})+W

**FLOW WORK**

#### It includes the work during

#### (i) Suction

#### (ii) Compression

#### (iii) Discharge

#### It is applicable to a compressor, turbine, pump and a nozzle.

#### Mathematical form of Flow Work = ∫ (–vdp) = γ (p_{2}v_{2} — p_{1}v_{1})/(γ – 1) kJ/kg

#### This flow work is γ times the non flow work.

#### As per the law of conservation of energy, input = output gives the steady flow energy equation(SFEE).

**m**_{i }(u_{i} +P_{i}v_{i} +C_{i}^{2}/2 + gz_{i})+Q = m_{0 }(u_{0} +P_{0}v_{0} +C_{0}^{2}/2 + gz_{0})+W

_{i }(u

_{i}+P

_{i}v

_{i}+C

_{i}

^{2}/2 + gz

_{i})+Q = m

_{0 }(u

_{0}+P

_{0}v

_{0}+C

_{0}

^{2}/2 + gz

_{0})+W

#### therefore, this equation is applicable for an ideal or real fluid, liquids, gases , compressible and in-compressible.

#### Now using mi = mo and h =u+Pv

#### we get _{ }(h_{i} +C_{i}^{2}/2 + gz_{i})+q = _{ }(h_{0} +C_{0}^{2}/2 + gz_{0})+w

_{ }(h

_{i}+C

_{i}

^{2}/2 + gz

_{i})+q =

_{ }(h

_{0}+C

_{0}

^{2}/2 + gz

_{0})+w

#### q =Q/m and w =W/m

#### Steady flow energy equation can also be written on per unit time basis as given below:

**(h**_{i} +C_{i}^{2}/2 + gz_{i})+q^{.} = _{ }(h_{0} +C_{0}^{2}/2 + gz_{0})+w^{.}

_{i}+C

_{i}

^{2}/2 + gz

_{i})+q

^{.}=

_{ }(h

_{0}+C

_{0}

^{2}/2 + gz

_{0})+w

^{.}

**q**^{.} — w^{.} = _{ }(h_{0} +C_{0}^{2}/2 + gz_{0}) — (h_{i} +C_{i}^{2}/2 + gz_{i})

^{.}— w

^{.}=

_{ }(h

_{0}+C

_{0}

^{2}/2 + gz

_{0}) — (h

_{i}+C

_{i}

^{2}/2 + gz

_{i})