Gas turbine brayton cycle thermodynamic mass flow rate of air

In summary: You need to find out how much mass is flowing through the system over that 1 second time period.In summary, the problem asks for the mass flow rate of air in a gas turbine designed to produce 3000hp using air at a maximum inlet temperature of 650K and assuming a heat loss of 70 kJ/s. The desired exhaust temperature is 200 degrees Celsius. The 1st Law, ΔU=Q-W, could be used to solve for the mass flow rate, but further information is needed about the time period.
  • #1
joesall
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Homework Statement



a gas turbine is designed to produce 3000hp when using air at a maximum inlet temperature of 650k and assuming a heat loss of 70 kj/s. if the exhaust temperature is desired to be no greater than 200 degrees celsius, determine the mass flow rate of air required.

Homework Equations


in the textbook the only things i can find are this formula
Qadd = mcp(t3-t2)
or Qrej = mcp (t1-t4)

but the problem is that solving with these with Qadd/cp(t3-t2) I am not sure if that would be correct using the figures given in this problem because it gives you an exhaust temperature and a max inlet temp.

The Attempt at a Solution



im having trouble coming up with the needed equation to determine the mass flow rate. any infromation would be highly appreciated as to the formula needed to find the mass flow rate.
 
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  • #2
joesall said:

Homework Statement



a gas turbine is designed to produce 3000hp when using air at a maximum inlet temperature of 650k and assuming a heat loss of 70 kj/s. if the exhaust temperature is desired to be no greater than 200 degrees celsius, determine the mass flow rate of air required.

Homework Equations


in the textbook the only things i can find are this formula
Qadd = mcp(t3-t2)
or Qrej = mcp (t1-t4)

but the problem is that solving with these with Qadd/cp(t3-t2) I am not sure if that would be correct using the figures given in this problem because it gives you an exhaust temperature and a max inlet temp.

The Attempt at a Solution



im having trouble coming up with the needed equation to determine the mass flow rate. any infromation would be highly appreciated as to the formula needed to find the mass flow rate.
Welcome to PF! Say, it's rather weird that they threw in HP along with all the metric units -- plus they used both K and °C -- but so be it.

It would seem that the 1st Law, ΔU=Q-W, should work here. You know what Q and W are for, say, a 1 second time duration.
 

Related to Gas turbine brayton cycle thermodynamic mass flow rate of air

1. What is the Gas Turbine Brayton Cycle?

The Gas Turbine Brayton Cycle is a thermodynamic cycle used in gas turbine engines to convert chemical energy, typically from a fuel source, into mechanical energy. The cycle consists of four main processes: compression, heat addition, expansion, and heat rejection.

2. How does the Brayton Cycle work?

The cycle begins with air being compressed in a compressor, increasing its pressure and temperature. The compressed air then enters a combustion chamber where fuel is added and ignited, causing a rapid increase in temperature and pressure. The high-pressure, high-temperature gas then expands through a turbine, producing mechanical energy to power the compressor and any external loads. Finally, the exhaust gas is released, completing the cycle.

3. What is the thermodynamic mass flow rate of air in the Brayton Cycle?

The thermodynamic mass flow rate of air in the Brayton Cycle is the rate at which air flows through the engine. It is typically measured in kilograms per second and is determined by the engine's design and operating conditions.

4. How is the mass flow rate of air related to the efficiency of the Brayton Cycle?

The mass flow rate of air is directly related to the efficiency of the Brayton Cycle. A higher mass flow rate indicates a greater amount of air entering the engine, which can result in a higher power output. However, a higher mass flow rate also requires more fuel to maintain the same temperature and pressure levels, which can decrease the overall efficiency of the cycle.

5. What factors affect the mass flow rate of air in the Brayton Cycle?

The mass flow rate of air in the Brayton Cycle can be influenced by several factors, including the engine's design, operating conditions, and size. Other factors such as temperature, pressure, and fuel type can also impact the mass flow rate. Additionally, the efficiency of the compressor and turbine can affect the amount of air that flows through the engine.

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