(1) Determine the velocity at the inlet of the diffuser
To determine the velocity at the inlet, the specific volume of the air
needs to be first determined. Since the air in the tunnel is an ideal
gas, it obeys the idealgas equation of state.
Pv = RT
where
R = 287 J/(kgK) for air
v = specific volume of the air
The specific volume can be determined at the inlet conditions:
v_{1} = RT_{1}/P_{1 }= 287(273+10)/80,000 =
1.015 m^{3}/kg
The velocity can be calculated using the following equation:
v_{1 }= v_{1}/A_{1
} =200(1.015)/1.5 =135.3 m/s
(2) Determine the temperature at the exit of the diffuser
Under the stated assumptions and observations, the energy balance for
the steadyflow through the diffuser can be expressed as
(h_{2}  h_{1}) + ( v_{2}^{2}  v_{1}^{2})/2 = 0
h_{2} = h_{1}  ( v_{2}^{2}  v_{1}^{2})/2
The enthalpy of air at the diffuser inlet can be determined from the
air table to be
h_{1} = h_{@283 k} = 283.14 kJ/kg
Assume the velocity at the exit is 0, then the enthalpy reaches the
maximum value.
h_{2} = 283.14  ( 0^{2} 
135.3_{}^{2})/2/1,000 = 292.3 kJ/kg
From the air table, the temperature corresponding to this enthalpy
value is
T_{2} = 292 K = 19^{o}C < 35 ^{o}C
which shows that the air is safe to exhaust to the outside environment.
