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Magic865

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- TL;DR Summary
- I am trying to find the forces acting on a raincap mounted on a pipe with a known mass airflow flowing through the pipe, but I am getting 2 different equations depending on whether I use Bernoulli's equation or Reynold Transport Theorem. Scenario 1 is with the cap closed, scenario 2 is with the cap open at angle theta. Attached is my work.

Hi,

I am trying to map out the forces that act on a raincap installed at the end of a pipe, but I have ran into a problem where I am getting 2 different equations depending on the method that I use. I'm definitely missing something here and I was hoping someone is about to point it out to me.

Consider the case where there is a hinged raincap at the end of a pipe with a known mass air flow going through the pipe. Assuming no viscous effects, I was hoping to find the force of the airflow acting on the raincap as it exits.

For my first scenario, I considered the cap fully closed and wanted to find the stagnation pressure of the airflow on the inside of the endcap (I was interested to see the worst-case scenario to see if the airflow would be capable of opening the raincap). To do this, I used Bernoulli's equation and assumed that all of the dynamic pressure of the airflow is converted to static pressure. I then took that pressure multiplied by the area of the cap to find force.

I then wanted to consider the case where the raincap is open at some angle theta. To do this, I used a simplified Reynolds Transport Theorem (RTT), took an angled control surface such that the flow entering from the pipe and the angled flow leaving after being deflected by the raincap are both perpendicular to the control surface. Assuming no losses (I'm looking for a relatively rough value here), I took the flow entering the control volume as being equal to the flow exiting. For the flow entering, there is only a y-component (v), for the flow existing, I found the x and y components with respect to theta. Completing the equation, I get a very similar result to what I had when using Bernoulli's principle, however there is a factor of 1/2 missing. This is more obvious if you assume theta is very small and sin(theta) approaches 0.

This doesn't make sense to me; why would the pressure be greater when assuming that all of the dynamic pressure becomes static versus when the flow still continues to move. I have definitely done something wrong here.Attached is my work.

I am trying to map out the forces that act on a raincap installed at the end of a pipe, but I have ran into a problem where I am getting 2 different equations depending on the method that I use. I'm definitely missing something here and I was hoping someone is about to point it out to me.

Consider the case where there is a hinged raincap at the end of a pipe with a known mass air flow going through the pipe. Assuming no viscous effects, I was hoping to find the force of the airflow acting on the raincap as it exits.

For my first scenario, I considered the cap fully closed and wanted to find the stagnation pressure of the airflow on the inside of the endcap (I was interested to see the worst-case scenario to see if the airflow would be capable of opening the raincap). To do this, I used Bernoulli's equation and assumed that all of the dynamic pressure of the airflow is converted to static pressure. I then took that pressure multiplied by the area of the cap to find force.

I then wanted to consider the case where the raincap is open at some angle theta. To do this, I used a simplified Reynolds Transport Theorem (RTT), took an angled control surface such that the flow entering from the pipe and the angled flow leaving after being deflected by the raincap are both perpendicular to the control surface. Assuming no losses (I'm looking for a relatively rough value here), I took the flow entering the control volume as being equal to the flow exiting. For the flow entering, there is only a y-component (v), for the flow existing, I found the x and y components with respect to theta. Completing the equation, I get a very similar result to what I had when using Bernoulli's principle, however there is a factor of 1/2 missing. This is more obvious if you assume theta is very small and sin(theta) approaches 0.

This doesn't make sense to me; why would the pressure be greater when assuming that all of the dynamic pressure becomes static versus when the flow still continues to move. I have definitely done something wrong here.Attached is my work.