A sphere of radius R and relative density 4 is hanging with the help of a string such that it remains just inside water. The ratio of force exerted by the liquid on upper and lower half of the sphere is (take Patm = 0)
When you calculate the force on the surface, you look at it from the surface of the projection. In this case, the curved surface is projected as a vertical plane, with centroid calculated for a rectangle/square. Remember, the triangle on the surface represents the pressure distribution and not the horizontal force. I hope that made sense (and I also hope I am right)
p deals with centroid so it's 6/2=3 ft , he dealed with it as a square of length 6ft in the direction up and 6ft in left direction making full imaginary square . i think .
Kinda late but yes, force P is acting from that far away but when it comes to calculating moment P must be acting onto a “surface” perpendicular to the force, which is why it doesn’t matter how far away P is across the X direction, moment about point H only changes if P changes distance in the Y direction because force P is perpendicular to the Y axis
Not quite my friend. FP doesn’t act on the centroid but rather on the center of pressure and on the right side of the gate you have air so that pressure must be taken into account.
+Michael Robledo Well, the body of water that we "took out" to draw our FBD does exert a force downwards that is resisted by the vertical reaction of the hinge (which we treat as a pin connection). Hope that answers your question!
answer will be 20217.6 lb exactly.... but this much calculation is not required . If we observe the free body diagram of gate properly we can solve in less than 15 sec... single stroke problem
Its just the choice of calculating the gage pressure (Pgage) or the absolute pressure (Pabs). Pabs = Patm+Pgage. In most of these problems, we consider the gage pressure and not the absolute pressure. So we don't have to add in the atmospheric pressure.
Probably too late to answer this but for people with the same question, You can assume it's a third of the way up from the hinge because the pressure distribution from the rest of the water in the tank creates a triangle shape on this point. We know that the centroid of a triangle is 1/3 from the fat end so we can say that is where the force is acting. He describes this as well, earlier in the video.
i don't know where you are confused at bro. but he did say that the force of the water was located "centroid of the pressure distribution". which is CP.
i guess it seems like you were confused on 9:20. where he solves for Fp. but equation of force of pressure is Gamma*Hc*A which Hc is the distance to the centroid of the surface from the surface of the water.
+Jonathan Teas We have three unknowns: P, Hx, and Hy. If we did the sum of forces in the x=0, we would still have three unknowns. Since two of the unknowns are at the hinge (Hx and Hy), the easiest thing to do would be take the moment about that point so you don't ever have to worry about Hx and Hy. :)
+Jonathan Teas You're right, Hy does not act in the horizontal direction. I meant that even after you summed any forces in the horizontal direction, you would still not know the values of Hx, Hy, or P (hence the three unknowns). You can sum the forces in the y direction to find Hy but you will still need a moment equation about any point and a sum of forces in the x direction to find the magnitude of force P. Or, like in this video, you can simply take the moment about the hinge and not have to worry about Hx or Hy. Hope this helps!
![Forces on Curved Surfaces: Example 2: Part 1 [Fluid Mechanics #54]](http://i.ytimg.com/vi/eiSWZUCbNyY/mqdefault.jpg)
![Forces on Curved Surfaces: Example 2: Part 1 [Fluid Mechanics #54]](/img/tr.png)
![Forces on Planar Surfaces: Example 2 [Fluid Mechanics #50]](http://i.ytimg.com/vi/OKOLvtogg24/mqdefault.jpg)
Really well explained, and a calm friendly voice to go with. Helped me out like crazy.
:)
Thank you so much man! Exact same problem is in my textbook, and chegg doesn't even solve it correctly, and then I find this video. Thank you!
I was literally stuck on this same problem! What a miracle, your the best!!!!!!!!!!!!!!!!!!!!!!
A sphere of radius R and relative density 4 is hanging with the help of a string such that it remains just
inside water. The ratio of force exerted by the liquid on upper and lower half of the sphere is (take Patm
= 0)
very nice hand writing
dude! thank you so much! I got critically confused from my textbook!
Hey man, how did you come up with a height of 3 ft from the surface in getting Fp??
I think it's 4 ft. 2/3 of 6 ft.
When you calculate the force on the surface, you look at it from the surface of the projection. In this case, the curved surface is projected as a vertical plane, with centroid calculated for a rectangle/square.
Remember, the triangle on the surface represents the pressure distribution and not the horizontal force.
I hope that made sense (and I also hope I am right)
i think u r not correct
p deals with centroid so it's 6/2=3 ft , he dealed with it as a square of length 6ft in the direction up and 6ft in left direction making full imaginary square . i think .
Lalitha Prasad yes you are correct
fun fact : the gate still hold the water even after 8 years
I can confirm that the gate is still indeed holding the water to this day. 😊
you didn't really need to calculate the moment if there is just an horizontal component on P right?
Thanks for the videos :D
Thank you so much this cleared up a lot for me!
For quarter circle given centriod is at 2r/3pie
You're awesome man
Thank you so much ! Very Helpful !
Video çok güzel olmuş. Teşekkür ederim
such a life saver! :)
can you find Weight W of water using (rho)(V)(g) and still get the same weight?
yes
you are awesome!
Thanks
Thank you so much
thanks, it helps a lot :D
Where is the reaction force acting on the water caused by the gate?
Thank uuuuuuuuuu
why don't you consider the force caused by the water in the half circle?
Thank you!
you are the best :)))))
wouldn't the force P be acting 6*Sqrt2 away from the hinge based on 45degree triangle hypotenuse?
Kinda late but yes, force P is acting from that far away but when it comes to calculating moment P must be acting onto a “surface” perpendicular to the force, which is why it doesn’t matter how far away P is across the X direction, moment about point H only changes if P changes distance in the Y direction because force P is perpendicular to the Y axis
Not quite my friend. FP doesn’t act on the centroid but rather on the center of pressure and on the right side of the gate you have air so that pressure must be taken into account.
Air on both sides cancels
we dont have the same answer in P tho we have the same value of Wh20 and Fp. can you please recompute for your P? ty
Is there no vertical force the gate exerts on the water? Does the hinge take place of that force?
+Michael Robledo Well, the body of water that we "took out" to draw our FBD does exert a force downwards that is resisted by the vertical reaction of the hinge (which we treat as a pin connection). Hope that answers your question!
The top of the 1/4 Circle is at the Surface so no pressure Downward.
And why isn't there a horizontal reaction by the gate?
what if the gate has weight?? 50kN the weight of the gate.. how to fine P?
I'm not seeing how you got to that value for P with the summation of moments that you've given. I've got something on the order of 10^5.
answer will be 20217.6 lb exactly.... but this much calculation is not required . If we observe the free body diagram of gate properly we can solve in less than 15 sec... single stroke problem
thanx a lot..
sir what is use of 4r/3pie
It is the centroid ofa quarter of a circle
Why is you assume the atmospheric pressure equal to 0?
Its just the choice of calculating the gage pressure (Pgage) or the absolute pressure (Pabs). Pabs = Patm+Pgage. In most of these problems, we consider the gage pressure and not the absolute pressure. So we don't have to add in the atmospheric pressure.
Why can you make the assumption that your Fp is a third in distance down the base of the surface when you're calculating the moments
Probably too late to answer this but for people with the same question,
You can assume it's a third of the way up from the hinge because the pressure distribution from the rest of the water in the tank creates a triangle shape on this point. We know that the centroid of a triangle is 1/3 from the fat end so we can say that is where the force is acting.
He describes this as well, earlier in the video.
I find it hilarious that the only part i didnt get was when you were looking the vol
very helpful! Thank you!
nice ah bro
how do you get the distance 2 ft from hinge for Fp? thanks
+domoto88 the centroid of a triangle is 1/3 the length.
🌹
this is wrong man
the force on plane surface does not act on the centroid but ao hc+(((a)(b^3)/12)/(A)(hc))
i don't know where you are confused at bro.
but he did say that the force of the water was located "centroid of the pressure distribution". which is CP.
i guess it seems like you were confused on 9:20. where he solves for Fp.
but equation of force of pressure is Gamma*Hc*A which Hc is the distance to the centroid of the surface from the surface of the water.
Where did get 6 ft and the area
him
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Ooops 😂
If u want to know study pattern then see Indian study channal in civil engineering .
Dear lord jesus why not just do summation of forces in the x=0?
+Jonathan Teas We have three unknowns: P, Hx, and Hy. If we did the sum of forces in the x=0, we would still have three unknowns. Since two of the unknowns are at the hinge (Hx and Hy), the easiest thing to do would be take the moment about that point so you don't ever have to worry about Hx and Hy. :)
Hy does not act in the horizontal direction...
You can do summation of forces in the y direction to find Hy too.
+Jonathan Teas You're right, Hy does not act in the horizontal direction. I meant that even after you summed any forces in the horizontal direction, you would still not know the values of Hx, Hy, or P (hence the three unknowns). You can sum the forces in the y direction to find Hy but you will still need a moment equation about any point and a sum of forces in the x direction to find the magnitude of force P. Or, like in this video, you can simply take the moment about the hinge and not have to worry about Hx or Hy. Hope this helps!
thanks it's Very helpful..n u r soo gay "Oops" 😁😁