Question 1

If the velocity potential can be described by

Φ = -b/4 (x-y)(x +y)

where b is some constant, what is the formula for the stream function? Sketch the flow pattern.

Question 2

The following measurements have been taken at sea level for a model aeroplane whose propeller had a diameter of 20 cm and was flying at 54 km/hr:

(a) Assume that viscous effects are negligible

(i) Plot this data using appropriate dimensionless groups

(ii) Determine the thrust of a similar aeroplane whose propeller has a 1.3 m diameter, spinning at 1500 rpm while flying at 300 ktn/hr at 3250 m altitude.

(b) Repeat pall (a) assuming that viscous effects are dominant.

Question 3

A petrol tanker uses gravity to empty its 35 kL tank into an underground storage tank. The hose that is used has a roughness equivalent to galvanised iron, has an internal diameter of 10 cm and is 10 m long (see figure). The centreline of the square hose fitting on the tanker is mounted 50 cm off the ground, while the hose penetrates 2 m below ground level. All bends have a radius of curvature of 15 cm. It is claimed that the tank can be emptied within 30 min: verify whether this claim is correct.