FIRST LAW APPLIED TO FLOW PROCESSES
Steady Flow Process
In a flow if fluid properties do not change with time at any given location, the process is steady flow process.
A_{1}, A_{2} — crosssection of stream, (m^{2})
m_{1}, m_{2} — mass flow rate, (kg/s)
p_{1}, p_{2} — pressure, (absolute), (N/m^{2})
v_{1}, v_{2 }— specific volume, (m^{3}/kg)
u_{1}, u_{2} — specific internal energy, (J/kg)
V_{1}, V_{2} — velocity, (m/s)
Z_{1}, Z_{2} — elevation above an arbitrary datum, (m)
dQ/dt— net rate of heat transfer through the control surface, (J/s)
dW_{x}/dt—net rate of work transfer through the control surface, (J/s)
t – time(s)
Now,
By conservation of mass
m_{1} = m_{2}
m_{1}, m_{2} — mass flow rate entering and leaving the control volume.
u= internal energy per kg of fluid
C= velocity of fluid
a)For one fluid stream SFEE (per unit time) is used.
b)For more than one fluid stream SFEE (per unit mass) is used.
c)Application of SFEE is steady flow processes
Nozzless & Diffusers
where, h is in kJ/ kg
Throttling Device
Throttling device is the generic name of any device or process that simply dissipates pressure energy m˙pv by irreversibly converting it into thermal energy. Unlike nozzles and diffusers, throttling devices provide no form of useful energy recovery.
z_{1} = z_{2}, V_{1}, V_{2} are negligible
h_{1} = h_{2}
Turbine and Compressor
Turbine is the device in which fluid expands. During the expansion work will be done by the fluid to drive, for example, electric generation. In this case, power output occurs.
Compressor is the device which is used to compress the fluid and increase its pressure. That means power input is required.
The change of kinetic energy and potential energy of fluid flowing into and out of turbines and compressors are very small that can usually be neglected:
(e_{kin})_{out }– (e_{kin})_{in}≈0 → c^{2}_{out }– c^{2}_{in}≈0
(e_{pot})_{out }– (e_{pot})_{in}≈0 → g•(z_{out }– z_{in})≈0
Turbine and compressors are also regarded as steadyflow engineering device, so the term at the righthand side equals zero:
Furthermore, m_{out}=m_{in} because of conservation of mass.
So now we obtain a simplified expression for turbine and compressor:
q+w+ h_{in }– h_{out}=0
where:
As discussed above,
= (h_{1}  h_{2}) for turbine
= (h_{2}  h_{1}) for compressor
Heat Exchanger
z_{1} = z_{2}, V_{1}, V_{2} are negligible
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