Q7 (10 Marks) Ship Stability 🔥 Repeated 5x in exams
SC&S • Written Exam

What is Prismatic Co-efficient (Cp).

(a) Derive the formula Cp = Cb/Cm, where Cb = Co-efficient of fineness and Cm = midship section area co-efficient.

(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 co-efficient 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 fresh water.

Appeared In: Feb 2021Oct 2020Oct 2019Aug 2019Feb 2019

Verified Model Answer (Text Solution)

Structured for DG Shipping MEO Class II examination scoring criteria.

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Part (a)

Prismatic coefficient is the ratio of the volume of displacement to the product of length and area of the immersed portion of the midship section

Cb is the block co-efficient or co-efficient of fitness is the ratio of the volume of displacement to the product of length, breadth and draught

$$\because\space C_{b}\space=\space{{\nabla}\over L\times B\times D}\:---\:1$$

$$C_{p}\space=\space{{\nabla}\over L\times A_{m}}\:---\:2$$

$$C_m \space = \space {{A_m} \over B \times D}$$

$$A_{m}=\:C_{m}\times B\times D\:---\:3$$

Substitute 3 in 2

$$C_{p}\space=\space{{\nabla}\over C_{m}\times B\times D\ \times L}\:---\:4$$

$$\nabla=C_{b}\times L\times B\times D\:---5\:\left(from\:equation\:1\right)$$

Substitute 5 in 4

$$C_{p}=\frac{C_{b}\times L\times B\times D}{C_{m}\times L\times B\times D}$$

$$C_p \space = \space {{C_b} \over C_m}$$

Part (b)

$$Length \space of \space ship \space = \space L$$

$$Draught \space = \space {{L} \over 18 }$$

$$breadth \space = \space 2.1 \times draught \space = \space 2.1 \times {{L} \over 18}$$

$$TPC\:in\:SW\:=\:0.01025A_{w}$$

$$TPC\:in\:FW\:=\:0.0100A_{w}$$

$$0.01025A_{w}-0.0100A_{w}=0.7$$

$$A_{w}=\frac{0.7}{2.5\times10^{-4}}=2800$$

$$C_w \space = \space {{A_w} \over L \times B}$$$$0.83 \space = \space {{2800} \over L \times {{2.1L} \over 18}}$$

$$L=170.04m$$

$$TPC\:in\:FW=0.010\times A_{w}$$

$$=\:0.0100\times2800$$

$$TPC\:in\:FW=28$$

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