CARDIFF SCHOOL OF ENGINEERING
EN1917 PROFESSIONAL ENGINEERING
LABORATORY REPORT: CENTRE OF PRESSURE
STUDENT NUMBER:
STUDENT NAME (1st 3 lette
DATE OF EXPERIMENT:
DATE OF SUBMISSION:
21127316
1 1. Abstract:
By doing an experiment using the centre of pressure, it is possible to demonstrate that
hydrostatics force and weight are similar in measurement using the theory of force in a flat
submerged surface. Weights are applied to push the scale over its pivot point, and water is
then poured to bring it back to level. Findings and data show that there is a linear
relationship between theoretical and experimental hydrostatic pressure force for the
partially submerged surface as well as the fully submerged.
Table of contents
1. Abstract.....
2. Introduction...
3. Theory......
4. Procedure.
5. Results....
6.
Discussion........
7. Conclusion........
8. References....
.2
.2
.3
2. Introduction
The pressure that a fluid exerts at a particular spot inside the fluid as a result of gravity is
known as hydrostatic pressure. With increasing depth, hydrostatic pressure rises
proportionately (EDinformatics, 1999). The experiment focuses on balancing and calculating
the hydrostatic moments and the weight masses to establish the theoretical and centre of
pressure along with the hydrostatic forces occurring on both partly and fully submerged
bodies. If at 10 degrees angle, the hydrostatic moment is straight and angled vertically when
being both submerged and not submerged, the theory would be accurate.
2 3. Theory
Hydrostatic pressure:
P = pgh = wh
The centre of pressure is made to measure the static hydrostatic force that a fluid exerts on
a submerged surface (Jasim, 2022). The equivalent of the pressure applied at the liquid's
surface needs to be added in order to measure the absolute pressure at depth:
Pa = Ps + P = Ps + wh
The moment applied is not proportional to the water height when the plane is partly
submerged since the water only covers a section of its surface. On the other hand, water
covers the whole area of the plane when it is fully submerged, hence the moment applied.
Should be inversely proportional to the water height (Araydah, 2019).
Calculations:
a=0°; M₁ = mg R3
Fully submerged:
h₁ = R1-x and h₂ = R2 - X
hG= (h1+ h2)/2
a=0°; M₁ = mg R3
Partly submerged:
h = R₂-x
hG=h/2
A = h B
A = (R2 - R1) B
F = rghGA
F = rghGA
=
hp (IG/A hG) + hG where IG = B D 3/12
hp = (2/3) h
DLA = x + hp
M2 = F DLA
(Millington, 2022)
DLA = x + hp
M2 = F DLA
a = 10°; M₁ = mg R3 cos a
Fully submerged:
h₁ = R1 cos a-x and h₂ = R2 cos a - x
hG (h1h2)/2 and LG = hG / cos a
=
A = (R2 - R1) B
a = 10°; M1 = m g R3 cos a
Partly submerged:
h = R2 cos a-x
hG=h/2
A = (h/ cos a) B
3 F = rghGA
hp = cos a [(IG / A LG) + LG] where IG = B D 3 / 12
DLA = (x + hp)/cos a
F = rghGA
hp = (2/3) h
DLA = (x + hp) / cos a
M2 = F DLA
(Millington, 2022)
M2 = F DLA
4. Procedure
Foot screws and bubble level were used to set the apparatus on a flat Surface. An empty
weight hanger was used to suspend the support. Because of the disturbance in balance,
water was added to the quadrant to level the tank and make sure the submerged plane was
vertical and at Omm. A beaker and syringe were used to add water to the quadrant until the
0° point was achieved in order to regain balance. The surface and the distance between the
pivot point were measured in mm. The stages were repeated along the way while the
weight was steadily raised by increments of 40g up to 560g. Results were obtained and
recorded after repeating the process at a 10° angle.
Sliding
weight
m
R1
R2
R3
Plane of
breadth, B
Levelling bubbles
0
Levelling
foot-screws
X
Quadrant
Figure 1: Centre of pressure apparatus (Millington, 2022)
4 5. Results
Table 1. Centre of pressure on a plane, vertical, unsubmerged immersed surface
Observations
Theory: Partially Submerged
Weight
Mass
Distance
from pivot to
Depth to
Water
moment
Water
depth
Depth to
centroid
Area
Force
centre of
moment
Lever arm
surface
pressure
HG=[h+(R1-
F=p g
hp= (2/3)
DLA=x+hp
M2=FL
m
M1= mgR3
X
h=R2-x
A=h
x)]/2
hGA
g
Nm
mm
m
m
M²
N
m
m
Nm
40
0.0981
161
0.039
0.0195
0.00293
0.56
0.0260
0.187
0.105
80
0.1962
144
0.056
0.0280
0.00420
1.15
0.0373
0.181
0.209
120
0.2943
130
0.070
0.0350
0.00525 1.80
0.0467
0.177
0.318
160
0.3924
119
0.081
0.0405
0.00608 2.41
0.0540
0.173
0.418
200
0.4905
110
0.090
0.0450
0.00675 2.98
0.0600
0.170
0.507
240
0.589
100
0.100
0.0500
0.00750 3.68
0.0667
0.167
0.613
Distance to water surface from pivot, x[mm]
180
160
140
120
100
80
60
40
40
20
0
40
80
80
120
160
200 240 280
Mass, m [g]
320
360 400 440
Figure 2: Vertical plane: distance to water surface from pivot point(x) for varying mass(m)
5/n Guidelines
Hygro Lab
Determination of the pore structure within concrete is a key indicator of its long-term durability.
Where density is the substances mass per unit volume and open porosity works on the assumption
water penetration and as a result potential contaminant. This is particularly relevant for steel
that internal pores are all connected. A higher porosity and therefore, lower density allows increased
reinforced structures where chloride penetration and can induce electro-chemical corrosion of the
reinforcement. Due to the reinforcement being embedded in the cementitious matrix, steel
degradation goes unnoticed resulting in a tensile structural failure.
Materials
of a
traditional kiln dried clay brick, autoclaved aerated concrete (AAC) block and dense concrete block
all shown in figure 1. Further guidance can be found in British Standard BS EN 12390-7:2009 Testing
hardened concrete Part 7: Density of hardened concrete (British Standards Institution 2009). The
samples provided have been oven dried at 60 °C for 5 days and allowed to cool to ambient
temperature prior to your lab.
Figure 7:
Two concrete
block section
Clay brick
Autoclaved
aerated
concrete
(AAC)
Equipment required
This experiment requires:
·
Testing materials (clay brick section, aerated block section, two concrete block section).
• Scales.
Measurement device (ruler or callipers).
• Bucket half full of water.
•
Dry cloth.
Archimedes tank with stirrup.
Experimental Procedure
Ensure the scales are zeroed and dry prior to taking mass values.
·
For each sample record its name width (w), depth (d) and height (h).
• Take and record the dry mass (mary) of all three samples individually using the scales.
Place the samples into the bucket of water and leave for one hour.
Move to experiment two, Sorptivity whilst the samples saturate.
•
Remove excess water by patting dry the saturated samples with the cloth.
Place the now saturated samples individually onto the scales and record the saturated mass
(msat).
Place the saturated mass on the stirrup into the density frame and record the Archimedes
mass (mArc).
Answer the problems in the worksheet.
66 Hygro Lab
Density and Porosity Log
Data and analysis
Enter the initial specimen dimensions to the nearest 0.1 mm in the following table:
Specimen
Width, w (mm)
Depth, d (mm)
Height, h (mm)
Volume (mm³)
Concrete
61
95
215
1245 925.0
concrete 2
62
98
213
1294188.0
clay
63
99
127.70 7920 99.6
AAC
64
98
214
1342268,0
Record the mass of each specimen to the 2nd decimal point.
Specimen
Dry mass, mary (g) Saturated mass, msat
(g)
Archimedes mass, marc
Concrete 250.0
277366
(g)
1534,8
Concrete
2605.3
282440
1537.5
clay
1937.1
15.21.8
844.7
A AC
92 4.7
1189.3
Calculate the bulk density, matrix density and open porosity values using the formulae provided
below. Check units carefully. Formula provided below. Note: Pw = 997
m3
can use pw = 1000
Formula
1-Volume: V=
msat-mArc
Pw
2 Bulk density Pbulk
=
msa mdry
V
*
mdry
3-Matrix density Pmat
=
Vmatrix
4- Volume of pores V pores
msat-mdry
Pw
5- Total Volume Vtotal = Vpores + Vmatrix
Vpores
6-Open porosity (Po
V
Using the formulae above, calculate the bulk density, matrix density and open porosity in the table
below.
msat
217736
m Dry
mArc
67
1.5348
21824
1.5218
1.1893
2.57
1.4371
0.9247
1.5375
2.6053
0.8447 4
Specimen
Bulk density, Pbulk
(kg/m³)
Hygro Lab
Matrix density, Pmat
(kg/m³)
Open Porosity o
(-)
Concreate
2067.5
2474.0
0.164
Concrete
2019.6
2433.3
0.17
Clay
2162
2418.7
0.125
1
A AC
1
4
5
VT
Vpore
Vmatriy
1 1.243×10-3 2.042×10
-3
2 1.290×10 2.193 × 10-
3 6.791 × 10 4 8.495 × 10 5 01903 1.0707 × 103
5.9415×10
-4
-4
07799
1.0388×103
2.653 x 104
68
99 M
Assessment questions
might they be different?
Hygro Lab
1. How does the volume experimentally determined compare to that by measurement? Why
To compare the clay
VT
6,791 × 10-4 m³
7,920 x 10 x m³
it's diffrent frow what we expected
initally in our
in our first caculation at may be because
of the unperfect shape
sh
1
aperfect
ари
2. Compare the open Porosity of the samples. What do your results tell you?
The 1 concreate has 0.164 open porosity
while the 2 concreate has oil? this
mean that 2. concreat has
a larger particle
Size which mean it's have a higher open
porosity
69
69 Hygro Lab
Experiment 2 -Sorptivity
Guidelines
Sorptivity testing measures the water uptake through capillary rise within a pore structure over time.
open porosity. Sorptivity testing can be used to measure to characterise the resistance to ingress
The sorptivity rate can be affected by mineralogical composition of the sample but predominantly the
additionally, it can be used to determine the healing potential of concrete. Sorptivity testing falls into
two stage primary and secondary, for this lab you will only consider primary. Unsaturated flow theory
shows that porosity is due to capillary forces which are greatest on dry specimens and become
negligible on saturated.
Materials
This experiment determines the sorptivity rate which is the height of absorption over the square root
of time. The samples (Clay brick section, Autoclaved aerated concrete (AAC) section, two concrete
block section) provided have been oven dried at 60°C for 5 days and allowed to cool to ambient
temperature prior to your lab (Figure 2).
Clay brick
Two concrete block
section
Autoclaved aerated
concrete (AAC)
Figure 2- Testing materials for sorptivity
Equipment required
This experiment requires:
Testing materials (clay brick section, aerated block section, two concrete block section)
•
•
Scales
Measurement device (ruler or callipers)
• Plastic water tray
Sample supports (washers)
•
•
Water
Stopwatch
Cloth
Equipment and Procedure
1. For each sample record its name as well as width (w), depth (d) and height (h).
2. Place the plastic water tray on a flat, level surface.
3. Place a washer under each corner of every sample inside the plastic water tray, ensure correct
spacings.
4. Pour water into the container to 5.0 ± 1.0 mm above the washers.
5. Record the dry mass of each specimen.
70
70
