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:
|
Propeller speed (rpm)
|
2400
|
3000
|
4500
|
|
Thrust force (N)
|
4.2
|
5.4
|
8
|
(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.