EXPERIMENT NO – 3

Date of conductionDate of SubmissionMarks Obtained :Timely submission (05)Quality of journal (10)Level of understanding(10)Total Marks ( Out of 25)Sign of staff member

STUDY OF FLOATING BODIES

Aim:-

To determine metacentric height of a ship model under different loading conditions.

Theory:-

A body floating in a fluid is subjected to two forces i.e.

1. Weight W of the body acting trough center of gravity G of the body.2. Upward buoyant force FB acting at the center of buoyancy B and is equal to the weight

of the liquid displaced by the body.

For a body to be in equilibrium, W = FB and both weight of the body and the buoyant force are acting along the same vertical line. When the body is tilted through a small angle θ (angle of heel) by two movable weights placed across the deck, the center of buoyancy shifts from B to B1 to the right and there is a parallel shift of the total center of gravity of the body. This shifting is due to the fact that the portion of body immersed on the right hands side increases while on left hand side decreases. If the vertical line is drawn through the new position of buoyant force through B1, it will intersect the initial line of action of buoyant force through point B at point M. this M is known as metacentre and the distance GM is called the metacentric height. The metacentric height is a measure of the static stability of the floating bodies.

The metacentric height is obtained by equating the moment due to movement of movable weights and the moment due to shifting of G to G1 and is given by expression:

GM = (W1 x1 – W2 x2) W tanθ

Where, W1 and W2 are the movable weights, x1 and x2 are the distances of W1 and W2

from the center of the cross bar respectively, W is the total weight of the ship model including the movable weights and θ is the angle of tilt.

Experimental Setup:-

The experimental set-up consists of a ship model which is allowed to float in a MS tank having a transparent side. The removable steel strips are placed at the bottom for changing the weight of the model. A cross bar is provided at the center of the model. On this cross bar, two weights are suspended for tilting the model. These weights can be placed at unequal distances with respect to the center of the cross bar so as to tilt the model. Pendulum and graduated arc are suitably fixed at the center of the cross bar. The angle of tilt is measured on a graduated arc by using pendulum consisting of a weight suspended to a long pointer.

Procedure:-

1. Fill the water tank two third and find out the weight of ship model to get W.

2. Displace the movable masses across the bar so s to tilt the model through the small angle θ.

3. Note the distances x1 and x2 from the center of cross bar and angle θ.

4. Repeat the above procedure for different weights of ship model by changing number of steel strips at the bottom of ship model.

Observation:-

1. Weight of ship model = W=

2. Weight of movable mass = W1=

3. Weight of movable mass = W2=

4. Unit weight of water = ρg =

5. Weight of ship No. 1 = weight of empty ship + weight of 1 No. of steel. Strip =

6. Weight of ship No. 2 = weight of empty ship + weight of 2 Nos. of steel. Strip=

7. Weight of ship No. 3 = weight of empty ship + weight of 3 Nos. of steel. Strip=

8. Weight of ship No. 4 = weight of empty ship + weight of 4 Nos. of steel. Strip=

9. Weight of ship No. 5 = weight of empty ship + weight of 5 Nos. of steel. Strip=

Observation table:-

Sr. No.

Weight of the ship

(gm.)

x1 x2 x2- x1

(m.)

θ(degrees)

tanθ Metacentric height ,GM

(m.)

Average metacentric

height.

1

2

3

4

5

Result: -

1. Average metacentric height of Ship A. = 2. Average metacentric height of Ship B. = 3. Average metacentric height of Ship C. = 4. Average metacentric height of Ship D. = 5. Average metacentric height of Ship E. =

Conclusion:-