Metacentric height of Floating Body


Aim: To ascertain the Metacentric height and radius of gyration of specified floating body

Equipment:

  • Stopwatch
  • Weights for tilt: 200,300, 500 gms
  • Float tank of the size 0.8*0.8*0.3
  • Ship with the arrangement to ascertain the tilt because of diversion of small weight

Basics:

The float is diverted for an angle of  from its level location by insertion of a undersized additional weight w on one face of the deck of the float at a space of ‘x’ cm commencing the middle of the deck. The meta centric height, GM (the space among the main point of gravity and the meta center is assessed as:

Where

w – The small extra weight in gm included on the deck.

W – The weight of the float in gm.

x- The space of weight w from the center, calculated the length of

The deck, in cm.

– The angle of the tilt assessed in degrees.

and  are the angle of tilt calculated, when the mass w is positioned on duck at a space of x cm from middle to the left and right sides correspondingly. The radius of gyration of the float is assessed by marking the time period taken for one free fluctuation of the float.

Radius of gyration

Where

T – The mean time for one oscillation in seconds.

GM– Meta centric height in cm at 0of tilt (specified from the graph.)

Process:

  1. Fill up the float tank with liquid for approximately ¾thof height and obtain the preliminary analysis of height.
  2. Keep the float into level position by putting the screw on the tilt- altering the nuts on exterior or interior so that it facilitates the plumb line passes all the way through the zero mark of the tilt-measuring appliance.

iii. Put a undersized weight w1 on one side (say left) of the float deck at a space of of x1(cm) from the middle of the deck. Note the  exposed by the plumb line.

  1. Shift the weight w1to the other side (right) of the deck for a distance of Xcm from the middle and mark the tilt as specified by the plumb line as ?R0.
  2. Replicate the steps 3 and 4 for two more spaces (x2cm and x3cm) and additional small weight w2, for getting six sets of readings.

Observation:

Level of water in the tank – Y1

Level of water in the tank with vessel – Y2

Volume of Water displaced = Y2 – Y1 x Area of the tank, cm3

Mass of the vessel Volume of water displaced x Density of water, gms

 

Metacentric height

Position of Weight Sl. No. Weight, gms Distance moved in cm Angle of Tilt  Applied Moment gm-cm Metacentric Height, MG, cm Metacentric Height at 0oangle of tilt
Weight on right side
Weight on left side

 

Radius of Gyration

Sl. No Tme for 5 Oscillations. Period for one Oscillation,

T secs.

Mean T
1

2

3

4

5

 

Result:

Inference: