EXPERIMENT 2: HYDROSTATIC PRESSURE
Objectives
•
•
To determine the hydrostatic thrust acting on a plane surface immersed in water when
the surface is partially and fully submerged.
To determine the position of the line of action of the thrust and to compare the
position determined by experiment with the theoretical position.
Introduction and Theory
The apparatus, shown in Figure 1, permits the moment due to the fluid thrust on a submerged
plane surface to be measured directly and compared with the theoretical analysis.
Figure 1: Hydrostatic Pressure Apparatus
When the quadrant is immersed in water it is possible to analyse the forces acting on the
surfaces of the quadrant as follows:
• The hydrostatic force at any point on the curved surfaces is normal to the surface and
therefore resolves through the pivot point because this is located at the origin of the
radii. Hydrostatic forces on the upper and lower curved surfaces therefore have no net
effect.
• The forces on the sides of the quadrant are horizontal and cancel out (equal and
opposite)
• The hydrostatic force on the vertical face is counteracted by the balance weight. The
resultant hydrostatic force on the face cab therefore be calculated from the value of the
balance weight and the depth of the water as follows:
When the system is in equilibrium, the moments about the pivot point are equal:
mgL = Fh
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2
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Methodology
Equipment Set Up
1. Measure the dimensions B (width) and D (height) of the quadrant end-face and the
distance H (height to pivot) and L (length of arm).
2. Position the Hydrostatic Pressure apparatus on a suitable level surface, then adjust the feet
until the spirit level indicates the apparatus is level in both planes.
3. Position the balance arm on the knife edges and check that the arm is free to swing.
4. Locate the empty weight hanger in the groove at the end of the balance arm.
5. Move the counter-balance weight until the balance arm is horizontal, indicate by the
central index mark on the beam level indicator.
Procedure
1. Add a small mass (typically 50g) to the weight hanger.
2. Close the drain valve and slowly add water to the tank using a jug.
3. Fill the flotation tank with water until the balance arm rises. Avoid wetting the balance
arm or the quadrant above the water level in the tank.
4. Continue to add water until the balance arm is horizontal (check this by aligning the flat
of the balance arm with the central mark of the level indicator.
5. When the arm is horizontal read the depth of immersion from scale on the face of the
quadrant. Allow for the water to settle before taking readings.
6. Repeat the above procedure for a different load increments by adding further weights to
the weight hanger. Use 50 g as interval.
7. Measure the water temperature.
Results
Fill in Tables 1 with measured and calculated values.
Table 1
Mass
added
Depth
Hydrostatic
Thrust
m
(g)
d
(mm)
F
(N)
#
Distance of
Centre of Pressure
Turning Moment
Experimental
Theoretical
Experimental
Theoretical
h1
h2
M1
M2
(m)
(m)
(Nm)
(Nm)
1
…
Conclusions
a) Comment on the variation of thrust with depth.
b) Comment on the relationship between the depth of the centre of pressure and the depth of
immersion.
c) Comment on and explain the discrepancies between the experimental and theoretical
results for the depth of centre of pressure.
d) Plot the experimental moment against theoretical moment. Comment on any relationships
noticed.
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