Moment of force exerted by water on tube

[TSny]

But the vertical air pressure force acting over the remaining part of the pipe does not change when fluid is flowing. So, if we include this in the vertical force balance on the pipe when fluid is flowing (together with the force from the fluid), the net downward force of the air $p_aA$ is just canceled out by the upward pressure force from the fluid $p_aA$. So the net resultant vertical force on the pipe when the fluid is flowing is just $2\rho v^2A$.

OK, that sounds good. I believe it is in line with what I was saying.

As far as the horizontal analysis is concerned, I will only note that the fluid pressure at the entrance cross section of the pipe is $p_a+(2\rho)g\frac{H}{4}$.

Should that be $p_a - (2\rho)g\frac{H}{4}$?

Virtually all the pressure changes leading up to the entrance cross section (exit cross section of the tank) occur within the tank.

Yes. Thanks for your comments!

 

[Chestermiller]

Should that be $p_a - (2\rho)g\frac{H}{4}$?

Yes. Sorry.

 

[Vibhor]

@TSny , Back to the liquid flowing through pipe . The problem is a very common one , water flowing out a straight pipe of cross sectional area A with speed 'v' .Find the force required to hold the pipe still .

Please see from 11.25 ,where the faculty discusses this .



I wonder how he uses dP/dt to calculate the force which turns out to be ρAv², whereas I believe that the answer should be 0 as there is no change of momentum of water coming out of the pipe .There should be no thrust from the water on the pipe .This also means that there should be no force required to hold the pipe still .

In the book as well similar result is derived as done in the above video .

Can this problem be modeled as a rocket problem ?

Please help me understand this .

Thanks .

 

[TSny]

I wonder how he uses dP/dt to calculate the force which turns out to be ρAv², whereas I believe that the answer should be 0 as there is no change of momentum of water coming out of the pipe .There should be no thrust from the water on the pipe .This also means that there should be no force required to hold the pipe still.

I agree with you that the outflow of the water from the end of the pipe does not create any force on the pipe. So, I agree that the treatment in the video is not correct. However, there might be a force required to hold the pipe in place depending on the overall shape of the pipe. For example, if the pipe contains an elbow just before you reach the end of the pipe, then the flow through the elbow would create a force on the pipe that would need to be balanced by an external force in order to keep the pipe in place.

The video's treatment of the elbow (staring around 15:40) looks ok to me.

Here's a short discussion that I think is essentially correct: http://link.springer.com/article/10.1007/s10694-014-0430-5

In this article there is a reference to a textbook by Fox which you can read here:
https://archive.org/details/IntroductionToFluidMechanicsFox8thEdition

Page 117 of this text has an example where the elbow is treated. However, it depends on equations derived earlier in the text.[/USER]