What is the tension in a bar submerged in water?

[TSny]

Yes. The formula that you gave for y_p assumes that the x-axis runs along the surface of the water.

For any orientation of the plane surface, imagine extending that plane in all directions. The extended plane will intersect the surface of the water along a straight line. That straight line corresponds to the x axis.

 

[foo9008]

Yes. The formula that you gave for y_p assumes that the x-axis runs along the surface of the water.

For any orientation of the plane surface, imagine extending that plane in all directions. The extended plane will intersect the surface of the water along a straight line. That straight line corresponds to the x axis.

what do you mean ?

 

[TSny]

what do you mean ?

The "extended plane" is just the infinite plane that the planar surface lies in. Take the door in your room. It is oriented vertically. That is, it is oriented in a vertical plane. If you imagined all four edges of the door becoming bigger and bigger until the edges are infinitely long, the door would become an infinite plane. That infinite plane is the infinite plane in which the original door was lying.

Likewise, if you took a planar surface of any shape then you can imagine the infinite plane in which the surface lies. If the planar surface is submerged in water, then the infinite plane in which the planar surface lies will intersect the surface of the water (unless the planar surface is horizontal).

In the case of the trough in your problem, the top edge of a rectangular side is already at the surface of the water. (No need for "extending the plane".) So, for that rectangular side, the top edge is the x-axis. See the picture below which shows the x-axis for the yellow rectangular side.

 

[TSny]

One thing that might be confusing is that the quantity $I_{xx}$ in the formula for $y_p$ represents the second moment of the area of the planar region about an axis that is parallel to the x-axis and that runs through the centroid of the planar area. It is not the second moment about the x-axis at the surface of the water.

 

[foo9008]

Yes. The formula that you gave for y_p assumes that the x-axis runs along the surface of the water.

For any orientation of the plane surface, imagine extending that plane in all directions. The extended plane will intersect the surface of the water along a straight line. That straight line corresponds to the x axis.

when you extend the line , the straight line that intersect with the water surface should be y-aixs , am right ? since we have yp ( center of pressure) , yc ( center of centroid) ...

 

[TSny]

when you extend the line

I was extending a planar region, not a line.

the straight line that intersect with the water surface should be y-aixs , am right ?

The extended plane intersects the surface of the water. The surface of the water lies in a horizontal plane. So, the intersection of the extended plane with the surface of the water corresponds to the intersection of two planes. Two planes intersect in a straight line. This straight line is the x axis.

The y-axis is perpendicular to the x-axis and the y-axis lies in the extended plane of the submerged planar surface. Yes, the y-axis will intersect the surface of the water at a point (the origin of the x-y coordinate system). As you move from the origin along the y axis, you move deeper into the water.

The first minute of the video that I linked to in post #43 explains the orientation of the x and y axes and the location of the origin. Can you pinpoint which part of the video that is not clear to you?

 

[foo9008]

I was extending a planar region, not a line.

The extended plane intersects the surface of the water. The surface of the water lies in a horizontal plane. So, the intersection of the extended plane with the surface of the water corresponds to the intersection of two planes. Two planes intersect in a straight line. This straight line is the x axis.

The y-axis is perpendicular to the x-axis and the y-axis lies in the extended plane of the submerged planar surface. Yes, the y-axis will intersect the surface of the water at a point (the origin of the x-y coordinate system). As you move from the origin along the y axis, you move deeper into the water.

The first minute of the video that I linked to in post #43 explains the orientation of the x and y axes and the location of the origin. Can you pinpoint which part of the video that is not clear to you?

ok , i think i gt the idea now . so , y-axis is the axis that bascially increases with the depth ?

 

[TSny]

ok , i think i gt the idea now . so , y-axis is the axis that bascially increases with the depth ?

Yes, that's right.