Solution Naval Numerical 1

Numerical 1: What is Prismatic Coefficient (Cp). (a). Derive the formula Cp=Cb/Cm; where Cb = Coefficient of fineness and Cm= midship section area coefficient.(b). The length of a ship Is 18 times the draught while the breadth is 2.1 times the draught. At the load water plane, the water plane area coefficient is 0.83 and the difference between the TPC in sea water and the TPC in fresh water is 0.7. Determine the length of the ship and the TPC in freshwater.

Solution: Prismatic Coefficient Is the ratio of the volume of displacement to the product of the length and the area of the Immersed portion of the mid-ship section.

(a). Derivation, 

we know that Block coefficient,

Cb= volume of displacement(∇)/Length(L) X Breadth(B) X Draught(d) And Prismatic coefficient,

Cp=volume of displacement(∇)/Length(L) X Area of Mid-ship section(Am) Thus; Cb/Cp=Am/B X d,(which is Cm)

Cb/Cp=Cm

or , Cp=Cb/Cm

(b) Let length of ship = L Then, Draught = L/18 And Breadth =2.1 X L/18

TPC sea water = 0.01025Aw

TPC fresh water = 0.0100 Aw., 

Given that the difference between the TPC in seawater and Freshwater is 0.7.

Thus, TPC sea water - TPC fresh water = 0.7 

0.01025Aw - 0.01000Aw. = 0.7 

0.00025Aw, = 0.7

Aw = 0.7/0.00025

Aw = 2800 m2

We know Cw=Aw/LXB

Given Cw=0.83 and B=2.1XL/18

Also Aw=2800m2

Now we can calculate length of the ship which is

L= 170m

and, The TPC in fresh water is 0.01Aw = 0.01X2800 =28 tonne.