The widths of a deep tank bulkhead at equal intervals of 1.2 m commencing at the top, are 8.0, 7.5, 6.5, 5.7, 4.7, 3.8 and 3.0 m. Calculate the load on the bulkhead and the position of the centre of pressure, if the bulkhead is flooded to the top edge with sea water on one side only.

The widths of a deep tank bulkhead at equal intervals of 1.2 m commencing at the top, are 8.0, 7.5, 6.5, 5.7, 4.7, 3.8 and 3.0 m. Calculate the load on the bulkhead and the position of the centre of pressure, if the bulkhead is flooded to the top edge with sea water on one side only.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 3.8

 

Solution:

width	SM	f(A)	Levers	FM	Levers	SM
8.0	1	8	0	0	0	0
7.5	4	30	1	30	1	30
6.5	2	13	2	26	2	52
5.7	4	22.8	3	68.4	3	205.2
4.7	2	9.4	4	37.6	4	150.4
3.8	4	15.2	5	76	5	380
3.0	1	3	6	18	6	108
		∑f(A) = 101.4		∑f(FM) = 256		∑f(SM) = 925.1

 

Load on bulkhead = ρg * FM

                              = ρg * h²/3 * ∑f(FM)

                              = 1.025 * 9.81 * 1.2²/3 * 256

Centre of pressure from top    = SM about top/ FM about top

                                                = (h³/3 * ∑f(SM)) / (h²/3 * ∑f(FM))

                                                = h * ∑f(SM) / ∑f(FM)

                                                = 1.2*925.6 / 256

                                                = 4.339 m