- #1

- 613

- 3

Part a is pretty easy

m'1+m'2=m'3

m'=mass flow rates

density1*velocity1*Area1+(analogous terms for inlet 2)=(analogous terms for inlet 3)

The 3 densities are unknown

but can be found from equation pressure/(RT)

R=286.9 J/(kgk)

This gives:

density 1=1.66 kg/m^3

density 2=1.432kg/m^3

density 3=2.35 kg/m^3

solving for mass flow rate gives 7.128 kg/s

not for part B our professor told us to use the equation

Q_dot_in - W_dot_out = m_dot_3 (cp T3 + V3^2/2 + gx3) - (analogous terms for 2) - (analogous terms for 1)

cp=specific heat =1004 J/kgK

h=cpT so that's where those terms came from

V1=Q1/A1

V2=Q2/A2

V3=Q3/A3

Where Q=volume flow rate given in the problem

this gives:

v1=86.61 m/s

v2=66.1m/s

v3=33.41 m/s

The equation also requires mass flow rates

mass flow rate = density*Q or density*velocity*area

m'1=4.98 kg/s

m'2=2.15 kg/s

m'3=7.128 kg/s

Now we have all the unknowns and the energy equation becomes

67-W_dot_out = 7.128 (1004*311+33.41^2 / 2 + 9.81*.5) - 2.15(1004*365 + .5*66.1^2+9.81*0.5) - 4.98(1004*294+.5*86.615^2+9.81*0)

W_dot_out = -118 kJ/s

W_dot_in = 118 kW

However the answer is supposed to be 223 kW or something like that.

I checked our my answer a few times and haven't found any mistakes. Can you guys check?

m'1+m'2=m'3

m'=mass flow rates

density1*velocity1*Area1+(analogous terms for inlet 2)=(analogous terms for inlet 3)

The 3 densities are unknown

but can be found from equation pressure/(RT)

R=286.9 J/(kgk)

This gives:

density 1=1.66 kg/m^3

density 2=1.432kg/m^3

density 3=2.35 kg/m^3

solving for mass flow rate gives 7.128 kg/s

not for part B our professor told us to use the equation

Q_dot_in - W_dot_out = m_dot_3 (cp T3 + V3^2/2 + gx3) - (analogous terms for 2) - (analogous terms for 1)

cp=specific heat =1004 J/kgK

h=cpT so that's where those terms came from

V1=Q1/A1

V2=Q2/A2

V3=Q3/A3

Where Q=volume flow rate given in the problem

this gives:

v1=86.61 m/s

v2=66.1m/s

v3=33.41 m/s

The equation also requires mass flow rates

mass flow rate = density*Q or density*velocity*area

m'1=4.98 kg/s

m'2=2.15 kg/s

m'3=7.128 kg/s

Now we have all the unknowns and the energy equation becomes

67-W_dot_out = 7.128 (1004*311+33.41^2 / 2 + 9.81*.5) - 2.15(1004*365 + .5*66.1^2+9.81*0.5) - 4.98(1004*294+.5*86.615^2+9.81*0)

W_dot_out = -118 kJ/s

W_dot_in = 118 kW

However the answer is supposed to be 223 kW or something like that.

I checked our my answer a few times and haven't found any mistakes. Can you guys check?