41.NA March 2019 Q.10(B)

The shaft power of a ship is 3000 KW, the ship’s speed V is 13.2 knot. Propeller rps is 1.27. Propeller pitch is 5.5m and the speed of advance is 11 Knots. Find: i. Real Slip ii. Wake fraction iii. Propeller thrust, when its efficiency, η = 70%

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Given

Sp = 3000 KW
V = 13.2 Knots
Rps = 1.27
P = 5.5 m
Va = 11 Knots

To find

1. Real slip, s
2. Wake fraction, w
3. Propeller thrust, T when its efficiency, η = 70%

Solution

RPM , N = Rps x 60
               = 1.27 x 60
               = 76.2

Theoretical speed Vt = P x N x 60/1852
                                  = 5.5 x 76.2 x 60/1852
                                  = 13.58 Knots

1. Real slip = [(Vt - Va) / Vt] x 100
                   = [(13.58 - 11) / 13.58] x 100
                s = 18.99 %

2. Wake fraction = (V - Va) / V
                           = (13.2 - 11) / 13.2
                       w = 0.167

3.  It is given that efficiency = 70 %
     Therefore Thrust power = Shaft power x Efficiency
                                            = 3000 x 0.7
                                            = 2100 KW

     Alternatively Thrust power = Thrust x Speed of advance
                                                 = T x Va
                                        2100 = T x 11 x (1852 / 3600 )
                                 Thrust  T = 2100 x 3600 / (11 x 1852)
                                                 = 371.09 KN