Many engineered structures -- such as dams,
valves,
marine vessels,
and locks --
involve surfaces that must resist hydrostatic pressures.
This model allows students to investigate these pressures
and measure the forces that they exert on various surfaces.
As we showed in one of our other videos,
the hydrostatic pressure P on a submerged surface increases with depth.
More specifically, it is given by the formula P = rho g h,
where rho is the mass density of the liquid,
g is the acceleration of gravity
and h is the height or depth of the water above the point we are considering.
As part of the design process, we often replace the pressure distribution on a particular surface,
like this valve face,
with an equivalent pressure force, Fp.
That force is equal in magnitude to the total force produced by the pressure,
and it acts at the center of gravity of the pressure distribution.
We call that point the "center of pressure."
The model allows students to measure
both the total pressure force Fp
on a submerged surface, and its position C.
The model has four panels of various shapes
and they are attached to a waterproof box
by flexible rubber membranes.
When the panel lies flush with the surface of the box,
the rubber membrane exerts no meaningful forces on it.
As a result, whenever a panel is flush with the box,
the applied external force Fe will
exactly match the magnitude and location
of the equivalent pressure force Fp.
As we fill the chamber with water,
you can watch the panels bulge out.
By trial and error, we find
the magnitude and location of the external force Fe
needed to push the panel back flush with the box.
Those values tell us the magnitude and location
of the equivalent pressure force Fp.
An important detail, is that we measure
the water depth D from the top of the panel
when the panel is flush with the box.
We do that because the depth changes a bit when the panel is moved in and out.
In this experiment,
the free surface of the water is 19.8 centimeters above the top of the circular panel.
The magnitude of the external force Fe is 23.3 Newtons,
and it must be applied
6 centimeters below the top of the panel
in order to balance the equivalent force
Fp from the internal pressure.
We developed a spreadsheet
that calculates the magnitude and location
of the equivalent pressure force.
To use it, we enter the panel diameter, which is 11 cm
and the water depth from the top of the panel,
and it is 19.8 cm.
The spreadsheet predicts an equivalent pressure force
of 23.6 Newtons
and it shows it shows its location
as being 5.8 cm below the top of the circular panel.
As you can see, these values are in good agreement
with our experimental measurements.
If you were designing a valve like this,
you would need force information of this kind
so you could properly size the actuator
and the top and bottom bearings.
The long membrane on the side of the box
allows students to feel
how the pressure varies with water depth.
If we lay the box on its side,
there is no depth change
from place to place along the membrane,
and the pressure is constant.
The pressure is uniform over any horizontal panel for the same reason.
Where would you expect the center of pressure to be for this horizontal triangular panel?
It would lie along the triangle centerline
and would be one-third of the distance from
the triangle base toward its apex.
Was your answer correct?
The model lets you carry out lots of other interesting experiments,
but this is what we have time to show you here.
We hope you learned something interesting
from this model
and that you will watch some of our other videos.