Simpson’s Rules may be used to find the areas and volumes of irregular figures. The rules are based on the assumption that the boundaries of such figures are curves which follow a definite mathematical law. When applied to ships they give a good approximation of areas and volumes.
Simpson’s rule is a numerical method that approximates the value of a definite integral by using quadratic polynomials.
The accuracy of the answers obtained will depend upon the spacing of the ordinates and upon how near the curve follows the law.
Simpson’s First Rule:-
This rule assumes that the curve is a parabola of the second order. A parabola of the second order is one whose equation, referred to co-ordinate axes, is of the form .
The end bulkhead of a deep tank 10m deep has the following horizontal ordinates at equal intervals, commencing from the top are 18.2, 16.7 and 15.6m resp. Find the thrust on the bulkhead if the tank contains SW to a sounding of 5m.
Please send me the solution