If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter

• Solids Fluids

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter 2/√π cm then the Reynolds number for the flow is (density of water = 10³ kg/m³ and viscosity of water = 10^-3 Pa.s) close to:

1. 5500
2. 11,000
3. 550
4. 1100

Solution

Reynolds number is given by

R = ρvd/η

The volume of the water flowing out per second is

Q = v × πd²/4

v = 4Q/d²π

R = ρvd/η

R = 4ρQ/πdη

ρ = Density of water = 10³ kg/m³

Q = 3 L / min = 3 × 10^-3 / 60 = 5 × 10^-5 m³/s

d = 2/√π × 10^-2 m = 1.125 × 10^-2 m

η = Viscosity = 10^-3 Pa.s

So, R = (4 × 10³ × 5 × 10^-5)/(3.14 × 1.125 × 10^-2 × 10^-3)

R ≅ 5500

The correct option is A.