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.