88.NA February 2020 Q.7(b)

A propeller 4.6 m diameter has a pitch of 4.3 m and boss diameter of 0.75. The real slip is 28% at 95 rev/min. Calculate the speed of advance, thrust and thrust power.

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Given

D = 4.6 m
P = 4.3 m
Db = 0.75 m
s = 0.28
N = 95

To find

1.The speed of advance, Va
2.Thrust, T 
3.Thrust power.

Solution

We know that theoretical speed Vt = P x N x 60/1852
                                                        = 4.3 x 95 x 60/1852
                                                        = 13.23 knot

1. Real slip = (Vt - Va) / Vt
       0.28 = (13.23 - Va) / 13.23
     3.704 = 13.23 - Va
     Speed of advance, Va = 9.525 knots

2. Effective disc area , A = (π/4) x (D2 - Db2)
                                        = (π/4) x (4.6² – 0.75²)
                                        = 16.18 m2

    Thrust T = የ x A x P2 x n2 x s
    n = rev /sec = 95/60 = 1.58

    Thrust T = 1.025 x 16.18 x 4.32 x 1.582 x 0 .28
                   =  215.2 kN

3. Thrust power = T x Va
                          = 215.2 x 9.525 x 1852/3600
                          = 1055 kW