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Q8. A model propeller is 0.4 m diameter and has a pitch of 0.4 m.

At a speed of advance of 2 m/s in water of density 1000 kg/m³ and at 6.8 revs/sec, the torque is 40 Nm and the thrust developed is 560 N.

A geometrically similar ship's propeller 5 m in diameter, is operating in water of density 1025 kg/m³ at corresponding linear and rotational speeds.

(a) Calculate EACH of the following for the ship's propeller:

(i) revolutions per second; (1)

(ii) speed of advance; (1)

(iii) real slip; (3)

(iv) delivered power; (3)

(v) propeller efficiency. (4)

(b) Calculate the hull efficiency when the propeller is operating on a vessel at a Taylor wake fraction of 0.25 and a thrust deduction fraction of 0.2. (4)

Note:  For similar propellers at corresponding speeds, it can be assumed:

Linear speed is proportional to (diameter)½

Rotational speed is proportional to (diameter)½

Thrust is proportional to (diameter)3

Torque is proportional to (diameter)4