Help with mass flow rate of turbine?

In summary: You need to get the specific volume at that point as well. Once you have that, you can calculate the mass flow rate using the given formula.In summary, the problem involves determining the mass flow rate of air through a turbine that expands air at 1300 kPa and 500oC to 100 kPa and 127oC. The air enters the turbine through a 0.2-m2 opening with an average velocity of 50 m/s, and exhausts through a 1-m2 opening. Using the formula PV=RT, the specific volume is calculated to be 0.17065 m^3/kg. However, the air has expanded after going through the turbine, so the specific volume at
  • #1
nate9519
47
0

Homework Statement


An turbine expands air at 1300 kPa and 500oC to 100 kPa and 127oC. Air enters the turbine through a 0.2-m2 opening with an average velocity of 50 m/s, and exhausts through a 1-m2 opening. Determine (a) the mass flow rate of air through the turbine

Homework Equations


PV=RT
m dot = (1/v)(V)(A)

The Attempt at a Solution


[/B]
I use PV=RT to get specific volume. (.287 * 773)/1300 = .17065 m^3/kg
I then plug it into the formula for mass flow rate which is (1/.17065)(50)(.2) = 58.6 kg/s
the problem is that the answer is suppose to be 46.9 kg/s but I can see anything I've done wrong. can someone help??
 
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  • #2
nate9519 said:

Homework Statement


An turbine expands air at 1300 kPa and 500oC to 100 kPa and 127oC. Air enters the turbine through a 0.2-m2 opening with an average velocity of 50 m/s, and exhausts through a 1-m2 opening. Determine (a) the mass flow rate of air through the turbine

Homework Equations


PV=RT
m dot = (1/v)(V)(A)

The Attempt at a Solution


[/B]
I use PV=RT to get specific volume. (.287 * 773)/1300 = .17065 m^3/kg
I then plug it into the formula for mass flow rate which is (1/.17065)(50)(.2) = 58.6 kg/s
the problem is that the answer is suppose to be 46.9 kg/s but I can see anything I've done wrong. can someone help??
Did you check what happens at the exhaust end? The air has expanded after going thru the turbine.
 

1. What is mass flow rate and why is it important in turbines?

Mass flow rate is the amount of mass passing through a certain point in a given amount of time. In turbines, it is important because it determines the amount of power that can be generated by the turbine.

2. How is mass flow rate calculated in a turbine?

Mass flow rate can be calculated by multiplying the density of the fluid by the velocity and the cross-sectional area of the turbine. This can be represented by the equation: Mass flow rate = Density x Velocity x Area.

3. What factors can affect the mass flow rate in a turbine?

The mass flow rate in a turbine can be affected by factors such as the size and design of the turbine, the type of fluid being used, and the operating conditions such as temperature and pressure.

4. How can the mass flow rate be increased in a turbine?

The mass flow rate in a turbine can be increased by increasing the fluid velocity, increasing the cross-sectional area of the turbine, or by using a more dense fluid. Additionally, improving the design and efficiency of the turbine can also increase the mass flow rate.

5. How does the mass flow rate affect the efficiency of a turbine?

The mass flow rate directly affects the efficiency of a turbine. A higher mass flow rate results in a higher power output, leading to a more efficient turbine. However, there is a limit to how much the mass flow rate can be increased before it starts to decrease the efficiency of the turbine.

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