Solving Homework Equations with Air Standard Assumptions

In summary, to solve for the velocity at the exit of the nozzle and the overall propulsion efficiency, you can use the isentropic relations and the equation W/Qin. The isentropic relations will allow you to calculate the velocity at the nozzle exit using the pressure and temperature at the nozzle inlet. The overall propulsion efficiency can be calculated by using the head addition and total energy input equations. To calculate the total energy input, you can use the mass flow rate, specific heat at constant pressure for air, and the temperatures at the nozzle exit and inlet. This can all be done using Air Standard assumptions.
  • #1
PenTrik
16
0
I usually try to avoid asking how to do entire question sets, but I'm officially at loss at the moment. I need a point in the right direction.

Homework Statement


I have a ramjet that has a velocity of 2500 km/h, pressure is 40 kPa, and temperature is 240K
Head addition is 1080 kJ/kG
Velocity at diffuser exit and nozzle inlet can be neglected

Homework Equations


Propulsion efficiency = W/Qin

The Attempt at a Solution


I need to solve for velocity at the exit of the nozzle, and overall propulsion efficiency.
I'm also supposed to use Air Standard assumptions. Does this help at all?

If this helps in solving the solution at all, I've solved for the pressure at the diffuser exit to be 457.47, with Pr as 7.268
 
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  • #2
and M as 0.5698.For the velocity at the exit of the nozzle, you can use the isentropic relations to calculate the velocity, given the pressure and temperature at the nozzle inlet (which, in this case, are the same as the diffuser exit). The isentropic relations are:P2/P1 = (T2/T1)^(k/(k-1)) V2/V1 = (T2/T1)^((k-1)/k) Where P2 and T2 are the pressure and temperature at the nozzle exit, respectively, and P1 and T1 are the pressure and temperature at the nozzle inlet. k is the ratio of specific heats for air. For the overall propulsion efficiency, you can use the equation W/Qin, where W is the head addition (1080 kJ/kG in this case), and Qin is the total energy input. To calculate Qin, you can use the equation Qin = m*cp*(T2-T1), where m is the mass flow rate, cp is the specific heat at constant pressure for air, T2 is the temperature at the nozzle exit, and T1 is the temperature at the nozzle inlet. Hope this helps!
 
  • #3


I would first clarify the specific equations that are needed for solving this problem. Based on the given information, it seems that the ideal gas law (PV = nRT) and the specific heat ratio for air (γ = 1.4) would be useful equations to use in this problem. Additionally, the specific thrust equation (F = m_dot * (V_exit - V_inlet) + (p_exit - p_inlet) * A_exit) may also be relevant in calculating the velocity at the exit of the nozzle.

Next, I would suggest breaking down the problem into smaller, more manageable parts. For example, start by calculating the mass flow rate (m_dot) using the given information and the ideal gas law. Then, use this value to calculate the specific thrust at the exit of the nozzle. From there, you can use the given head addition and the specific thrust equation to solve for the velocity at the exit of the nozzle. Finally, use the given information and the specific thrust equation to calculate the overall propulsion efficiency.

It may also be helpful to review the assumptions made in air standard analysis, such as assuming a perfect gas and neglecting any changes in kinetic and potential energy. These assumptions may affect the accuracy of the solution, so it's important to keep them in mind while solving the problem.

Overall, as a scientist, I would recommend breaking down the problem into smaller steps and using the relevant equations to solve for the desired values. It may also be helpful to consult a textbook or other resources for additional guidance on solving problems using air standard assumptions.
 

Related to Solving Homework Equations with Air Standard Assumptions

What are the air standard assumptions used in solving homework equations?

The air standard assumptions used in solving homework equations include assuming the air to be an ideal gas, constant specific heats, and neglecting the effects of friction and heat transfer within the system.

How do I determine the specific heats for air in homework equations?

The specific heats for air can be found in tables or equations provided in textbooks or online resources. The values may vary depending on the temperature and composition of the air.

Can I apply air standard assumptions to all types of homework equations?

No, air standard assumptions are typically used in thermodynamics problems involving gases. They may not be applicable to other types of equations, such as those involving liquids or solids.

What are the limitations of using air standard assumptions in solving homework equations?

The assumptions may not accurately represent real-world scenarios, as they neglect important factors such as friction and heat transfer. They are also limited to ideal gas behavior, which may not be the case in all situations.

How can I check if the air standard assumptions are valid for my homework equations?

You can check the conditions of your problem against the assumptions and see if they are a good approximation. If the problem involves high pressures or low temperatures, the assumptions may not be valid.

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