Solution Naval Numerical 32

Numerical 32: The following information relates to a model propeller of 400mm pitch

Revs/min	400	450	500	550	600
Thrust N	175	260	365	480	610
Torque Nm	16.8	22.4	28.2	34.3	30.5

(i) Plot curves of thrust and torque against rev/min 
(ii) When the speed of advance of the model is 150 m / min and slip 0.20, calculate the efficiency.
Solution:(i) curves of thrust and torque against rev/min 

Given: (ii) 
Va = 150m/min or 2.5m/sec. 
Slip =0.20

The theoretical speed of the propeller Vt= P x n
Pitch P=0.4
Vt = 0.4 x n m/sec
Slip = (Vt -Va)/Vt
Slip = (0.4n- Va)/0.4n
slip= 0.2 and Va = 2.5
(0.4n-2.5)/0.4n = 0.2
or n= 7.8125 rps or 468.75 RPM
At 468.75 RPM, Thrust = 320N
At 468.75 RPM Torque = 25.5 Nm
dp = Tx 2πn dp
at 458.75 RPM is 25.5X7.8125=1251 Nm
tp = T x Va
tp at 468.75 RPM is 320X 2.5=800 Nm
tp = dp x prop. efficiency.
Hence propeller efficiency = 80000/1251= 64%