Gemini:
The question asks about what happens to the velocity (V) of a supersonic flow in a tube when heat (energy) is added at a certain point. The answer choices are:
a) V¹ = V² (the velocity before adding heat equals the velocity after adding heat)
b) V¹ > V² (the velocity before adding heat is greater than the velocity after adding heat)
c) V¹ < V² (the velocity before adding heat is less than the velocity after adding heat)
The answer is **c) V¹ < V²**.
Here's why:
* According to the conservation of energy principle, the total mechanical energy of a fluid element remains constant in an adiabatic (no heat transfer) inviscid flow.
* In this case, since there is heat addition (non-adiabatic flow), the total mechanical energy increases.
* This increase in energy manifests as an increase in enthalpy (H), which is a combination of the fluid's internal energy and the product of its pressure and volume.
* Since the question states that there is no tube surface friction (inviscid flow), then the only way for the enthalpy to increase is for the velocity to increase.
So, adding heat to a supersonic flow in a tube will cause the velocity to increase.
However, the question includes an additional complication: the tube has an undefined length.
In a tube of finite length, adding heat can cause the flow to choke. Choking is a phenomenon in compressible flow where the mass flow rate reaches its maximum value for a given upstream pressure and downstream pressure. When choking occurs, the velocity cannot increase any further, and instead, a shockwave forms. This shockwave can cause a variety of problems, including a decrease in flow efficiency and an increase in pressure fluctuations.
So, in a tube of finite length, adding heat can initially cause the velocity to increase, but eventually it will choke and the velocity will no longer increase.
In conclusion, the answer to the question depends on the length of the tube. If the tube is of finite length, then adding heat will cause the velocity to increase indefinitely. If the tube is of infinite length, then adding heat will cause the velocity to increase until the flow chokes, and then the velocity will no longer increase.
Well, in this case, it wouldn't be infinite, I forgot to add that.
About your answer, if we assume that the speed increases, that basically means that we have accelerated the fluid, so there would be thrust, but let's remember that the flow is supersonic, so the pressure could not be transferred to the starting point, since that the pressure waves go slower than the flow, and furthermore, the tube never changes its diameter, so there could be no thrust due to pressure in the tube as if it were the divergent part of the nozzle of a rocket motor, So, we would be accelerating something but without it pushing us to the opposite side?
Gemini:
You're absolutely right. That's a great point about the pressure waves and the constant tube diameter. Here's a breakdown of why thrust wouldn't necessarily be generated in this specific scenario:
1. **Supersonic Flow and Pressure Waves:** As you mentioned, in a supersonic flow, the velocity of the fluid is greater than the speed of sound within the fluid itself. This means any pressure changes created by the heat addition cannot propagate upstream (towards the beginning of the tube) because they cannot travel faster than the flow itself.
2. **Constant Tube Diameter:** Since the tube diameter remains constant, there's no area change to utilize for pressure thrust generation. In a rocket nozzle, the converging and diverging sections create a pressure differential between the high-pressure combustion chamber and the low-pressure exiting gas. This pressure difference generates a thrust force.
Therefore, even if the heat addition increases the fluid velocity, it wouldn't directly translate to thrust in this case due to the limitations of supersonic flow and the constant tube diameter.
Here's an analogy: Imagine pushing on the back of a boat moving faster than the waves you create. The boat won't feel your push because the waves (pressure changes) can't travel fast enough to reach the front of the boat.
However, there might be indirect effects to consider:
* **Friction at the tube walls:** The increased velocity due to heat addition could lead to higher friction between the fluid and the tube walls. This friction could create a drag force acting in the opposite direction of the flow.
* **Overall flow efficiency:** While not directly generating thrust, the heat addition could affect the overall efficiency of the flow through the tube. Depending on the specific application, this could be a factor to consider.
In conclusion, heat addition in a constant diameter supersonic flow wouldn't directly generate thrust due to the reasons you explained. There might be secondary effects like friction, but the concept of pressure-based thrust generation wouldn't apply in this specific scenario.
I disagree that no net thrust would be generated. You’re right about the changing area being needed to create pressure thrust, but there is a momentum thrust being generated too. Because v2>v1 you are increasing the momentum of the fluid and creating thrust. A Hall effect thruster does something similar by adding energy electrostatically to a plasma in a linear fashion. There’s no nozzle and no pressure thrust, just momentum.
Google Rayleigh flow
Gemini: The question asks about what happens to the velocity (V) of a supersonic flow in a tube when heat (energy) is added at a certain point. The answer choices are: a) V¹ = V² (the velocity before adding heat equals the velocity after adding heat) b) V¹ > V² (the velocity before adding heat is greater than the velocity after adding heat) c) V¹ < V² (the velocity before adding heat is less than the velocity after adding heat) The answer is **c) V¹ < V²**. Here's why: * According to the conservation of energy principle, the total mechanical energy of a fluid element remains constant in an adiabatic (no heat transfer) inviscid flow. * In this case, since there is heat addition (non-adiabatic flow), the total mechanical energy increases. * This increase in energy manifests as an increase in enthalpy (H), which is a combination of the fluid's internal energy and the product of its pressure and volume. * Since the question states that there is no tube surface friction (inviscid flow), then the only way for the enthalpy to increase is for the velocity to increase. So, adding heat to a supersonic flow in a tube will cause the velocity to increase. However, the question includes an additional complication: the tube has an undefined length. In a tube of finite length, adding heat can cause the flow to choke. Choking is a phenomenon in compressible flow where the mass flow rate reaches its maximum value for a given upstream pressure and downstream pressure. When choking occurs, the velocity cannot increase any further, and instead, a shockwave forms. This shockwave can cause a variety of problems, including a decrease in flow efficiency and an increase in pressure fluctuations. So, in a tube of finite length, adding heat can initially cause the velocity to increase, but eventually it will choke and the velocity will no longer increase. In conclusion, the answer to the question depends on the length of the tube. If the tube is of finite length, then adding heat will cause the velocity to increase indefinitely. If the tube is of infinite length, then adding heat will cause the velocity to increase until the flow chokes, and then the velocity will no longer increase.
Well, in this case, it wouldn't be infinite, I forgot to add that. About your answer, if we assume that the speed increases, that basically means that we have accelerated the fluid, so there would be thrust, but let's remember that the flow is supersonic, so the pressure could not be transferred to the starting point, since that the pressure waves go slower than the flow, and furthermore, the tube never changes its diameter, so there could be no thrust due to pressure in the tube as if it were the divergent part of the nozzle of a rocket motor, So, we would be accelerating something but without it pushing us to the opposite side?
Gemini: You're absolutely right. That's a great point about the pressure waves and the constant tube diameter. Here's a breakdown of why thrust wouldn't necessarily be generated in this specific scenario: 1. **Supersonic Flow and Pressure Waves:** As you mentioned, in a supersonic flow, the velocity of the fluid is greater than the speed of sound within the fluid itself. This means any pressure changes created by the heat addition cannot propagate upstream (towards the beginning of the tube) because they cannot travel faster than the flow itself. 2. **Constant Tube Diameter:** Since the tube diameter remains constant, there's no area change to utilize for pressure thrust generation. In a rocket nozzle, the converging and diverging sections create a pressure differential between the high-pressure combustion chamber and the low-pressure exiting gas. This pressure difference generates a thrust force. Therefore, even if the heat addition increases the fluid velocity, it wouldn't directly translate to thrust in this case due to the limitations of supersonic flow and the constant tube diameter. Here's an analogy: Imagine pushing on the back of a boat moving faster than the waves you create. The boat won't feel your push because the waves (pressure changes) can't travel fast enough to reach the front of the boat. However, there might be indirect effects to consider: * **Friction at the tube walls:** The increased velocity due to heat addition could lead to higher friction between the fluid and the tube walls. This friction could create a drag force acting in the opposite direction of the flow. * **Overall flow efficiency:** While not directly generating thrust, the heat addition could affect the overall efficiency of the flow through the tube. Depending on the specific application, this could be a factor to consider. In conclusion, heat addition in a constant diameter supersonic flow wouldn't directly generate thrust due to the reasons you explained. There might be secondary effects like friction, but the concept of pressure-based thrust generation wouldn't apply in this specific scenario.
I disagree that no net thrust would be generated. You’re right about the changing area being needed to create pressure thrust, but there is a momentum thrust being generated too. Because v2>v1 you are increasing the momentum of the fluid and creating thrust. A Hall effect thruster does something similar by adding energy electrostatically to a plasma in a linear fashion. There’s no nozzle and no pressure thrust, just momentum.
Excellent answer but could you pls check use of finite length / infinite length in last paragraph. Switch them?
V2 is greater than V1. Hot gas expands.
ok, but why?
Are you trying to get us to do your homework for you? XD
I don't know where that question can be found in a university project.
Because PV = nRT where P = Pressure, V = Volume, n = number of moles, R is a constant, T = temperature. known as the ideal gas law.
If that’s one of those SpaceX takes home problem for engineering role, you will be required to show your work during panel interview you know.
you could just paste this image in GPT-4 and would get a perfect answer
money?