Solution Naval Numerical 7

Numerical 7:A ship of length 140m , Breadth of 18.5m, draught of 8.1m and a displacement of 17,025 tonnes in sea water, has a face pitch ratio of 0.673. Diameter of the Propeller is 4.8m. The results of the speed trial show that true slip may be regarded as constant over a range of 9 to 13 knots and is 30%, w = 0.5Cb-0.05. If fuel used is 20t/day at 13 knots and fuel consumption/day varies as cube of speed of ship, Determine the fuel consumption, when the propeller runs at 110 rpm.

Solution: Given that ships length (L) = 140m
Breadth(B) = 18.5m
Draught (d) = 8.1m
Displacement (Δ) = 17,025 tonne
Pitch ratio = 0.673
Diameter (D) = 4.8m
Slip is given constant within 9 to 13knots speed.(S) = 30% or 0.3
w = 0.5CB-0.05
Consumption = 20t/day at 13 knots.

N = 110rpm
Pitch ratio = Pitch/Diameter
Thus, The pitch of the propeller = 0.673 x 4.8 = 3.23m.
Theoretical speed = PN60/1852.
at 110rpm Vt = (3.23 x 110 x 60)/1852 = 11.56 knots.
The block coeff cb = △/LBdρ
Cb = 17025/(140 x 18.5 x 8.1) x 1.025 =0.78,
Hence w = 0.5 x 0.78 - 0.05 = 0.346
S = (Vt - Va)/Vt = (11.56 - Va)/11.56,
0.3 = (11.56 -Va)/11.56,
Va = 8.057 knots
We know that wake (w) = (V-Va)/V 
w = (1 - Va/V)
Ship speed (V) = Va/(1-w)
V = 8.057/(1-0.346)
V = 12.32 knots
Using the relation,  
Hence, consumption per day at 12.32knots =
=17.02tonne