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For the laminar flow of water oyer a sphere, the drag coefficient CF is defined as CF = F/(ρU²D²), where F is the drag force, ρ is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m³. When the diameter of the sphere is 100 mm and the fluid velocity is 2 m/ s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200 mm under dynamically similar conditions, the drag force (in N) on this sphere is _______.
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- 100N
- 18N
- 20N
- 40N
Correct Option: C
Drag coefficient,
Cf = | ||
ρU²D² |
F = CfρU²D²
For sphere –1
ρ1 = 1000 kg/m³
D1 = 100 mm = 0.1m
U1 = 2 m/s
CF = 0.5
For sphere –2
ρ2 = 1000 kg/m²
But D2 = 0.2m
Due to dynamically similar conditions:
(Re)1 = (Re)2
= | ||
v1 | v2 |
2 × 0.1 = U2 × 0.2
U2 = 1 m/s
F2 = CFρU²2D²2
F2 = 0.5 × 1000 × 1² × 2²
= 20N