HYDROSTATIC PRESSURE
The objective of this lab is to determine the position of the center of
pressure on the rectangular face of a toroid as seen in figure 1.
Figure 1: Hydrostatic Pressure Module
Technical data
The schematic of the module can be seen in figure 2
Figure 2: Schematic of Hydrostatic Pressure module
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Figure 3: Dimensions of Hydrostatic Pressure
For a partly submerged vertical plane surface:
Hyrdrostatic thrust F =
Bgd 2
2
(1)
Experimental position of the center of pressure h” =
2mL
Bd 2
Theoretical position of the center of pressure h” = h’ + H – d
(2)
(3)
For a fully submerged vertical surface:
Hydrostatic thrust F = gBD (d  D / 2)
(4)
Experimental position of the center of pressure h” =
Theoretical position of the center of pressure h” =
mL
BD (d  D / 2)
(5)
D 2 / 2  (d  D / 2) 2  H  d
(6)
d  D/2
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Method
1. Measure the dimensions B and D of the quadrant end face and the dimensions H
and L (see figure). Position the empty plastic tank on the bench. Ensure that the
toroid is located on the dowel pins and the central clamping screw is tightened.
Position the assembled balance arm on the knife edges.
2. Locate the weight hanger in the groove at the end of the balance arm. Ensure that
the drain valve is closed. Direct the free end of the hose connected to the drain
valve to the sink.
3. Level the tank using the adjustable feet and a spirit level. Move the counter-balance
weight until the balance arm is horizontal (flat underside of the balance arm level
with the beam level indicator).
4. Add water to the tank until it is full. Ensure that no water is spilled on the upper
surfaces or sides of the quadrant. Add all the weights to the weight hanger. Slowly
drain water from the tank using the drain valve until the balance arm is horizontal.
Read the depth of immersion from the scale on the side of the quadrant. More
accurate results can be obtained from reading below the surface, to avoid the
effects of surface tension.
5. Remove one of the 50 gram weights from the weight hanger. Drain the tank slowly
again until the balance arm is horizontal. Note the height reading carefully. Repeat
this step by removing one weight at a time.
Questions
1. Plot the thrust vs. depth of immersion (h vs d) and comment on the variation.
2. Plot the depth of immersion vs. the theoretical and experimental centers of
pressure, h”. Comment on the relation between h” and d.
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