A propeller 6m diameter has a pitch ratio of 0.9, BAR 0.48 and, when turning at 110 rev/min, has a real slip of 25% & wake faction 0.30. If the propeller delivers a thrust of 300 kN & the propeller efficiency is 0.65, calculate:
i. Blade area ii. Ship speed iii. Thrust power iv. Shaft power v. Torque
IF YOU ARE NOTICING ANY ERROR KINDLY COMMENT BELOW
Given
D = 6 m
p = 0.9
BAR = 0.48
N = 110
s = 0.25
w = 0.30
T = 300 kN
ηp = 0.65
To find
i. Blade area
ii. Ship speed
iii. Thrust power
iv. Shaft power
v. Torque
Solution
i) We know that BAR = Ad / {(π/4) x D2)
0.48 = Ad / {(π/4) x 62)
0.48 = Ad / 28.26
Blade area, Ad = 13.56 m2
ii) We know that pitch ratio, p = P / D
0.9 = P / 6
Pitch , P = 5.4 m
Theoretical speed , Vt = P x N
= 5.4 x 110
= 594 m/min = 9.9 m/sec
Real slip , s = (Vt - Va) / Vt
0.25 = (9.9 - Va) / 9.9
2.475 = 9.9 - Va
Speed of advance, Va = 7.425 m/sec
Wake fraction, w = (V - Va) / V
0.30 = (V - 7.425) / V
0.3 x V = V - 7.425
0.7 x V = 7.425
Ship speed , V = 10.60 m/sec = 10.60 x (3600/1852) = 20.60 knots
iii) We know that thrust power, tp = Thrust x Speed of advance
= 300 x 7.425
= 2227.5 kW
iv) We know that thrust power, tp = Delivered power x propeller efiiciency
2227.5 = dp x 0.65
dp = 3426.92
And shaft power , sp = dp / transmission efficiency
As in problem nothing mentioned about transmission efficiecy, it is considered as negligible.
So Shaft power , sp = 3426.92 kW
v) We know that dp = Torque x 2 x π x n
3426.92 = T x 2 x π x (110/60) {n = N/60}
3426.92 = T x 11.51
Torque , T = 297.73 kN m
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