Question

calculate the maximum velocity and the correspondingbvolumetric flow rate (in/cm^3/s) at which laminar flow of air and water is possible in pipes with the following diameter D=.25,.5,1.0,2.0,4.0,6.0, and 10.0in

Answer 1

For air at room temperature at 25 °C

Density of air = 1.1839 kg/m3

Viscosity of air = 1.84 x 10^-5 Pa-s

For Laminar flow, Reynolds Number Re = 2100

D = 0.25 in x 1m/39.37in = 0.00635 m

Re = diameter x velocity x density /viscosity

2100 = (0.00635 m x velocity x 1.1839 kg/m3) / (1.84 x 10^-5 Pa-s)

Maximum velocity = ( 2100 x 1.84 x 10^-5) / (0.00635 x 1.1839)

= 0.03263789 / 0.00635

= 5.14 m/s

Volumetric flow rate = area x velocity

= (3.14/4) x ( 0.00635 m)^2 x 5.14 m/s

= 0.00016269 m3/s x (100cm/1m)^3

= 162.69 cm3/s

D = 0.50 in = 2 x 0.25 in x 1m/39.37in = 2 x 0.00635 m

Maximum velocity = 0.03263789 / (2 x 0.00635)

= 2.57 m/s

Volumetric flow rate =area x velocity

= (3.14/4) x ( 2 x 0.00635 m)^2 x 2.57 m/s

= 0.00032539 m3/s x (100cm/1m)^3

= 325.39 cm3/s

D = 1.0 in = 4 x 0.25 in x 1m/39.37in = 4 x 0.00635 m

Maximum velocity = 0.03263789 / (4 x 0.00635)

= (5.14/4) = 1.285 m/s

Volumetric flow rate =area x velocity

= (3.14/4) x ( 4 x 0.00635 m)^2 x (5.14/4) m/s

= 0.00016269 x 4 m3/s x (100cm/1m)^3

= 650.69 cm3/s

D = 2.0 in = 8 x 0.25 in x 1m/39.37in = 8 x 0.00635 m

Maximum velocity = 0.03263789 / (8 x 0.00635)

= (5.14/8) = 0.6425 m/s

Volumetric flow rate =area x velocity

= (3.14/4) x (8 x 0.00635 m)^2 x (5.14/8) m/s

= 0.00016269 x 8 m3/s x (100cm/1m)^3

= 1301.52 cm3/s

D = 4.0 in = 16 x 0.25 in x 1m/39.37in = 16 x 0.00635 m

Maximum velocity = 0.03263789 / (16 x 0.00635)

= (5.14/16) = 0.32125  m/s

Volumetric flow rate =area x velocity

= (3.14/4) x (16 x 0.00635 m)^2 x (5.14/16) m/s

= 0.00016269 x 16 m3/s x (100cm/1m)^3

= 2603.04 cm3/s

D = 6.0 in = 24 x 0.25 in x 1m/39.37in = 24 x 0.00635 m

Maximum velocity = 0.03263789 / (24 x 0.00635)

= (5.14/24) = 0.2142 m/s

Volumetric flow rate =area x velocity

= (3.14/4) x (24 x 0.00635 m)^2 x (5.14/24) m/s

= 0.00016269 x 24 m3/s x (100cm/1m)^3

= 3904.56 cm3/s

D = 10.0 in = 40 x 0.25 in x 1m/39.37in = 40 x 0.00635 m

Maximum velocity = 0.03263789 / (40 x 0.00635)

= (5.14/40) = 0.1285 m/s

Volumetric flow rate =area x velocity

= (3.14/4) x (40 x 0.00635 m)^2 x (5.14/40) m/s

= 0.00016269 x 40 m3/s x (100cm/1m)^3

= 6507.6 cm3/s

For water at room temperature at 25 °C

Density of water = 997 kg/m3

Viscosity of water = 8.90 x 10^-4 Pa-s

For Laminar flow, Reynolds Number Re = 2100

D = 0.25 in x 1m/39.37in = 0.00635 m

Re = diameter x velocity x density /viscosity

2100 = (0.00635 m x velocity x 997 kg/m3) / (8.90 x 10^-4 Pa-s)

Maximum velocity = ( 2100 x 8.90 x 10^-4) / (0.00635 x 997)

= 0.0018746 / 0.00635

= 0.2952 m/s

Volumetric flow rate = area x velocity

= (3.14/4) x ( 0.00635 m)^2 x 0.2952 m/s

= 0.00016269 m3/s x (100cm/1m)^3

= 9.344 cm3/s

For different diameter of pipes max velocity and volumetric flow rate can be calculated as same as for air.