Link toMatlab m-file as text file(click browser "back" button to return here)

The file above has calculations for several sets of T and P. See a listing of current output at bottom of this page.Let's put the results in easy-to-remember terms. Here, consider the case of ambient conditions (1 bar, 300 K):

For flow in a 1 m-diameter tube:

The laminar-turbulent transition occurs at a mean flow velocity of 35 mm/s for air and 2 mm/s for water.

At the critical Reynolds number, the velocity varies inversely with tube diameter (velocity at transition is larger in smaller tube).

The volumetric flow rate at the critical Re is directly proportional to diameter (volumetric flow rate is smaller in smaller tube).

For air, the critical velocity decreases with increasing pressure and increases with increasing temperature.

For water, the critical velocity decreases with increasing temperature and doesn't change much with pressure.

For flow over a flat plate at 1 m/s:

The laminar region lasts reaches at least 1.5 m from the leading edge for air and 0.1 m for water (at Re = 1e5). At this point the velocity boundary layer thickness is 25 mm for air and 1.5 mm for water, and increases with the square-root of the distance from the leading edge.

As velocity increases, the transition point gets closer to the leading edge and, at a fixed distance from the leading edge, the boundary layer thickness decreases (both vary with square root of the reciprocal velocity).

For air, these lengths decrease with increasing pressure and increase with increasing temperature.

For water, these lengths don't change much with pressure and decrease with increasing temperature.

For air, the thicknesses of the velocity, concentration and thermal boundary layers are about the same.

For water, the concentration boundary layer is one-tenth the thickness of the velocity boundary layer, and the thermal (temperature) boundary layer is one-half the thickness of the velocity boundary layer.

(boundary layer ratios from del-v/del-c = Sc^{1/3}, and del-v/del-T = Pr^{1/3})

Schmidt number is about 1 for oxygen in air, 900 for ethanol in water (450 for carbon dioxide in water)

Prandtl number is about 0.6 for air, 6 for water

Current output in SI units, (1 bar & 300 K) (10 bar & 300 K) (1 bar & 500 K) These results need to be checked

ScAir =

0.9707 0.9707 0.9707

ScWater = (for ethanol in water)

892.8 892.8 57.6

PrAir = (these appear to be low)

0.5992 0.5497 0.0920

PrWater =

6.5548 6.5548 0.6430

U (m/s) and V (m3/s) flow rate in 1 m-diameter tube at laminar-turbulent transition (Re = 2200)

Uair =

0.0348 0.0035 0.0750

Uwater =

0.0020 0.0020 0.0002

Vair =

0.0274 0.0027 0.0589

Vwater =

0.0016 0.0016 0.0002

Distance from leading edge of flat plate for laminar-turbulent transition for bulk flow velocity of 1 m/s at Re = 5e5

Xair =

7.9199 0.7920 17.0408

Xwater =

0.4650 0.4650 0.0500

Boundary layer thicknesses (del) at the transition distance for velocity (V at 99% free-stream), concentration (C at thickness of stagnant film with equal flux), and thermal (T at thickness of stagnant film with equal flux)

delVair =

0.0560 0.0056 0.1205

delVwater =

0.0033 0.0033 0.0004

delCair =

0.0339 0.0034 0.0730

delCwater =

1.0e-003 *

0.2049 0.2049 0.0549

delTair =

0.0399 0.0041 0.1601

delTwater =

0.0011 0.0011 0.0002