The University of Jordan
Faculty of Engineering and Technology
Department of Civil Engineering
_________________________________________
Hydraulics Laboratory
0931363
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 1
 Objectives and Liabilities:
1- Determine experimentally the result hydrostatic force applied on a submerged
surface.
2- Determine the center of pressure.
 Apparatus:
The apparatus consists of a transparent rectangular water tank that supports a counter
balance arm. Attached to the counter balance arm is a toroid quadrant. The tank has a
drain at one end and a leveling screw at each corner of its base. On the top edge of the
tank are two knife-edge supports that hold the counter balance arm. The counter-balance
arm has an adjustable weight at one end and a weight pan at the other end. The arm is
balanced by the use of a level mounted in the middle of the arm. Finally, a hook gauge
mounted at one end of tank is used to measure water level.
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 2
 The resultant force is:
FDynamic = 0 , Because of there is no movement for water in the tank.
Where:
o P: pressure.
o A: area.
o Ρ: density of water ( the density of water = 1000
).
o g: acceleration of gravity ( the acceleration of gravity = 9.81
).
o hcg: center of gravity.
Where the shape of the force applied is triangle.
 The difference between center of pressure and center of gravity:
 Center of gravity:
The vertical depth from the water surface to the centroid of the water.
( ȳ = ).
Where:
o ȳ: center of gravity.
o y: water depth.
 Center of pressure:
The location of the line of action of the resultant hydrostatic force lies at a point.
hcp = ycp = ȳ +
Where:
o hcp = ycp: center of pressure.
o ȳ: Center of gravity.
o I: the moment of inertia or second moment of area
o A: area of tank.
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 3
 The situations of immersion of body.
1- Basic:
The water of surface is touching the bottom of body ( equilibrium status ) , where
the bubble of the machine in center of circle.
2- Partially immerged:
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 4
The location of the center of pressure is:
 Expermentaly:
–
(
–
)
Where:
o m: more weight.
o g: acceleration gravity.
o L: the distance from pivot to more mass>
o F: hydrostatic force.
o y: the depth of wate.
o d: the depth fo cross section.
o a:
 Theoretical:
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 5
3- Totally immerged:
 Expermentaly:
–
(
–
)
Where:
o m: more weight.
o L: the distance from pivot to more mass.
o F: static force.
o y: the depth of water.
o
d: the depth fo cross section.
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 6
o a:
 Theoretical:
Where:
o d: the depth of water.
o ȳ: center of gravity and its equal in this statement (
).
 Producing to do this experiment:
1- Make sure that the ( a, b, d and L ) are correct.
2- Level the tank using the adjustable feet in conjunction with the spirit level.
3- Adjustable the counter balance weight until the balance arm is horizontal; this is
indicated on a gate adjacent to the balance arm.
4- Pump water to the Perspex tank until the water is level with the bottom edge of the
toroid, and the tank venire reading.
5- Place a mass on the balance pan.
6- Raise the water surface in the tank until the balance arm is horizontal again.
7- The water level which restore the balance arm to its balanced position using the venire
gauge.
8- Add masses to the balance plan in cerements of 50grams, the repeat step 6 & 7.
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 7
 The calculation about this experiment:
ρ= 1000
, g= 9.81
, a= 10cm , L=30cm , d= 10cm , b= 7.5cm , I=
 y < d:
Partially:
At m= 100 gm
=
–(
– ) ( Experimental )
–
(
)
( Theoretical )
 y>d
Totally:
At m= 400gm
–(
(
– ) ( Experimental )
)
( Theoretical )
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 8
Status
Result NO:
Mass
(gm)
Depth y
(mm)
ȳ
(mm)
Force
(N)
y<d
y<d
y<d
y<d
y>d
y>d
y>d
y>d
1
2
3
4
5
6
7
8
50
100
150
200
250
300
350
400
47.1
67.4
84.6
99.1
112.4
125.1
150.1
163
23.55
33.7
42.3
49.55
56.2
62.55
75.05
81.5
0.816097579
1.671167835
2.632940235
3.612830479
4.64764446
5.757247429
8.288227429
9.774070875
hcp
(mm)
Exp
hcp
(mm)
Theo
27.40932064
31.4
43.50439469 44.93333333
52.26426907
56.4
62.01935187 66.066666667
70.70599916 71.02799526
72.4545346 75.87267519
74.3786843 86.15370864
83.44111559 91.72494888
 Discussion and Conclusion:
• From our results that the center of pressure is always deeper than the center of area.
• The center of pressure is affected by the depth of water, by increasing water level the
center of pressure increase (i.e. direct downward), but the center of area is constant, so
the difference between the two centers is increasing with the increase of water level.

Errors in this experiment:
1- The error in the measuring and reading.
2- The error in the level of the water.
3- The error due to unbalanced weights.
By: Qusai Waleed Al-Qudah · · · · · · · · · · · · · · 9