Center of Pressure: 2b/3 from Free Surface

[foo9008]

Homework Statement

can someone explain about the Fr acting at a distance 2b/3 from free surface firectly beneath the centroid of the surface ?

Homework Equations

The Attempt at a Solution

does the author mean the center if pressure ( point where the FR acts) of the completely submerged plate (90 degree) is at 2b/3 from the top of the surface ? p/s : the whole vertical length of the submerged surface is b

 

[CWatters]

does the author mean the center if pressure ( point where the FR acts) of the completely submerged plate (90 degree) is at 2b/3 from the top of the surface ? p/s : the whole vertical length of the submerged surface is b

Yes. When the top edge of the plate is at the surface Fr acts at a depth of 2b/3. If the plate sinks further Fr moves towards the centre of the plate (eg towards b/2).

See "2. COP Fully submerged plate"...

http://people.exeter.ac.uk/TWDavies...tic Force on a submerged vertical surface.htm

 

[foo9008]

Yes. When the top edge of the plate is at the surface Fr acts at a depth of 2b/3. If the plate sinks further Fr moves towards the centre of the plate (eg towards b/2).

See "2. COP Fully submerged plate"...

http://people.exeter.ac.uk/TWDavies/solid mechanics/Hydrostatic Force on a submerged vertical surface.htm

can you explain why in this case , the center of pressure not at 2/3 of the submerged plane ? if it's 2/3 , it should be 8= (1.2/3) = 8.8 m , right ? why the working only showed 8.61m?

 

[CWatters]

It's only at 2/3rds of the height of the plate when the top edge of the plate is at the surface. In the case of the car the top edge is 8m down.

I get the same answer using the equation in your notes...

y_p = s + b/2 + b²/(12(s+b/2)
= 8 + 1.2/2 + 1.2²/(12(8+b/2)
= 8 + 0.6 + 0.014
= 8.61m

and the equation at the link I posted..

= 2/3 * (y₂³ - y₁³)/(y₂² - y₁²)
= 2/3 * (9.2³ - 8³)/(9.2² - 8²)
= 2/3 * (778.69 - 512)/ (84.64 - 64)
= 2/3 * 266.69/20.64
= 8.61m

 

[foo9008]

the plate is at the s

It's only at 2/3rds of the height of the plate when the top edge of the plate is at the surface. In the case of the car the top edge is 8m down.

I get the same answer using the equation in your notes...

y_p = s + b/2 + b²/(12(s+b/2)
= 8 + 1.2/2 + 1.2²/(12(8+b/2)
= 8 + 0.6 + 0.014
= 8.61m

and the equation at the link I posted..

= 2/3 * (y₂³ - y₁³)/(y₂² - y₁²)
= 2/3 * (9.2³ - 8³)/(9.2² - 8²)
= 2/3 * (778.69 - 512)/ (84.64 - 64)
= 2/3 * 266.69/20.64
= 8.61m

so, when the top edges of the submerged object is located exactly at the water surface(s=0) , then the center of pressure of submerged object will be at exactly 2/3 of the height of the submerged object ?

 

[CWatters]

Yes. That's mentioned in your image dsc_0525-jpg.