Respuesta :
Answer:
a) The exit temperature is 430 K
b) The inlet and exit areas are 0.0096 m² and 0.051 m²
Explanation:
a) Given:
T₁ = 127°C = 400 K
At 400 K, h₁ = 400.98 kJ/kg (ideal gas properties table)
The energy equation is:
[tex]q-w=h_{2} -h_{1} +\frac{V_{2}^{2}-V_{1}^{2} }{2} +delta-p[/tex]
For a diffuser, w = Δp = 0
The diffuser is adiabatic, q = 0
Replacing:
[tex]0-0=h_{2} -h_{1} +\frac{V_{2}^{2}-V_{1}^{2} }{2} +0[/tex]
Where
V₁ = 250 m/s
V₂ = 40 m/s
Replacing:
[tex]0-0=h_{2} -400x10^{3} +\frac{40^{2}-250^{2} }{2} +0\\h_{2} =431430 J/kg=431.43kJ/kg[/tex]
Using tables, at 431.43 kJ/kg the temperature is 430 K
b) The inlet area is:
[tex]m=\frac{P_{1} }{RT_{1} } A_{1} V_{1} \\\frac{6000}{3600} =\frac{80}{0.287*400} A_{1} *250\\A_{1} =0.0096m^{2}[/tex]
The exit area is:
[tex]m=\frac{P_{2} }{RT_{2} } A_{2} V_{2} \\\frac{6000}{3600} =\frac{100}{0.287*430} A_{2} *40\\A_{2} =0.051m^{2}[/tex]
A) The exit temperature of air is; T₂ = 430 K
B) The inlet and exit areas of the diffuser are;
A₁ = 0.0096 m²
A₂ = 0.051 m²
A) We are given;
T₁ = 127°C = 400 K
V₁ = 250 m/s
V₂ = 40 m/s
From table A-17 attached which shows ideal gas properties of air, At a temperature of 400 K, h₁ = 400.98 kJ/kg = 400980 J/kg
Now, formula for the energy equation is;
q - w = h₂ - h₁ + ¹/₂(V₂² - V₁²) + ΔP
We are told that the diffuser is adiabatic and as such;
q = 0 and w = ΔP = 0
Thus;
0 - 0 = h₂ - 400.98 * 10 + ¹/₂(40² - 250²) + 0
0 = h₂ - 400980 - 30450
h₂ = 431430 J/kg = 431.43 KJ/kg
From the table attached, the temperature that corresponds to h₂ = 431.43 KJ/kg is T₂ = 430 K
B) To get the inlet area A₁, we will use the formula;
m = (P₁/RT₁) × A₁V₁
where;
m = 6000 kg/h = 1.67 Kg/s
P₁ = 80 kPa
R is a constant = 0.287 kJ/kg.k
T₁ = 400 K
V₁ = 250 m/s
Thus;
1.67 = (80/(0.287 × 400)) × (A₁ × 250)
Solving this gives;
A₁ = 0.0096 m²
For exit area;
m = (P₂/RT₂) × A₂V₂
where;
m = 6000 kg/h = 1.67 Kg/s
P₂= 100 kPa
R is a constant = 0.287 kJ/kg.k
T₂ = 430 K
V₂ = 40 m/s
1.67 = (100/(0.287 × 430)) × (A₂ × 400)
Solving this gives;
A₂ = 0.051 m²
Read more at; https://brainly.com/question/15729967
