Respuesta :
Answer:
The mass flow rate of air is 0.732 kg/s.
The velocity at the exit is 5.927 m/s.
Explanation:
Given that,
Diameter = 28 cm
Enter pressure= 200 kPa
Enter temperature = 20°C
Velocity = 5 m/s
Exit pressure = 180 kPa
Exit temperature = 40°C
We need to calculate the mass flow rate of air
Using formula of mass flow rate
[tex]\dot{m}=\rho\times \dot{V}[/tex]
[tex]\dot{m}=\dfrac{P}{RT}\times A\times v[/tex]
Put the value into the formula
[tex]\dot{m}=\dfrac{200}{0.287\times293}\times\dfrac{(0.28)^2}{4}\times\pi\times5[/tex]
[tex]\dot{m}=0.732\ kg/s[/tex]
We need to calculate the volume flow rate
Using formula of volume flow rate
[tex]\dot{V'}=\dfrac{\dot{m}}{\rho'}[/tex]
[tex]\dot{V'}=\dfrac{RT'\dot{m}}{P'}[/tex]
[tex]\dot{V'}=\dfrac{0.287\times313\times0.732}{180}[/tex]
[tex]\dot{V'}=0.365\ m^3/s[/tex]
We need to calculate the velocity at the exit
Using formula of velocity
[tex]v'=\dfrac{\dot{V'}}{A}[/tex]
Put the value into the formula
[tex]v'=\dfrac{4\times0.365}{(0.28)^2\times\pi}[/tex]
[tex]v'=5.927\ m/s[/tex]
Hence, The mass flow rate of air is 0.732 kg/s.
The velocity at the exit is 5.927 m/s.
