CE 3254 (HYDRAULICS LABORATORY EXERCISE 6)
I. TITLE: METACENTRIC HEIGHT OF FLOATING BODIES
II. OBJECTIVE(s):
1. To investigate the stability of the floating body in the laboratory.
2. To compare the righting couple calculated using the formula RC=W(MGsin) against the
couple calculated by translating a weight(W1) at distances of 1 cm from the center and by
computing the percentage difference.
III. MATERIALS NEEDED:
Metacentric Weight Apparatus, Pail or basin, Water, Wooden Platform
IV. THEORY:
Theory:
Consider a ship floating as shown in the figure. The center of gravity of the body is at G and the center of
buoyancy is at B. For equilibrium, the weight of the floating body is equal to the weight of the liquid it
displaces and the center of gravity of the body
and the centroid of the displaced liquid are in
the same vertical line. The centroid of the
displaced liquid is called the “center of
buoyancy”. Let the body now be heeled
through an angle ϴ. This would produce a new
position of the center of buoyancy after
heeling. A vertical line through the new Cg will
intersect the centerline of the body at M and
this point is known as the metacenter of the
body even the angle is diminishingly small.
The distance MG is known as the metacentric height. The force due to buoyancy acts vertically up B1 and
is equal to W. The weight of the body acts downward through G.
V. SEQUENCE OF OPERATIONS:
Laboratory Manual in Fluid Mechanics by Engr. Angelito A. Saluague, CE, MEP
1. Prepare all the materials needed for the experiment. Make sure the materials used are in good
condition.
2. Make sure that the space used in the laboratory is well lighted so that the measurements can be
made properly.
3. Weigh the boat to be used and determine the weight (W1) to be translated at intervals of 1 cm every
movement from the center of the boat.
4. Measure the height(H) and base(B).
5. Place the boat in water and make sure it is balanced. Make sure the plumb line reads initially 0o or
adjust it until it reads 0o when the weight W1 is at the center.
6. Measure the draft (D) of the boat for the calculations of MBo and MG.
7. Unscrew the load in the middle of the boat and place it in a distance 1 cm from the center or G.
8. Read the angle at every movement of W1 which is automatically graduated on the vertical face of the
line through G.
9. Repeat procedures 7 and 8 until W1 is moved 12 cm from the center.
10. Tabulate the values obtained. Compare values of righting couples calculated using the formula
RC1=W(MGsin)=BF(MGsin) against righting couples obtained by RC2=W1(dcos), where d is 1 cm, 2
cm, 3 cm, … until 12 cm.
11. Compute the percent difference as 100%(RC1-RC2/RC2.
ILLUSTRATION:
Laboratory Manual in Fluid Mechanics by Engr. Angelito A. Saluague, CE, MEP
VI. DATA AND CALCULATIONS with TABLES:
Ɵ
x
MBO
MG
Righting
Couple
(Kg.cm)
VII. REMARKS, HINTS, and PRECAUTIONS:
To ensure safety in the laboratory room, one must observe that laboratory rooms are absolutely
“no-smoking” areas. In case of fire, each must be aware of the location of the fire extinguishers.
Because of the imperfections present in the devices used, a load must be located that will more or less
make the boat float with horizontal base almost flat. The additional weight must be accounted for in the
assigning of the weight of the boat model. The draft must be measured as the average of the four drafts
at each corner of the model boat.
The plumb line must be steady for you to read the angles easily.
VIII. CONCLUSION
Laboratory Manual in Fluid Mechanics by Engr. Angelito A. Saluague, CE, MEP
Laboratory Manual in Fluid Mechanics by Engr. Angelito A. Saluague, CE, MEP