Flow Type
A Newtonian fluid with a dynamic viscosity of 0.05 lb/(ft∙s) and a density of 500 lb/ft^3 flows through a 0.25 ft diameter pipe with a velocity of 2 ft/s. Is the flow through the pipe characterized as laminar, turbulent, or transitional?
Expand Hint
Flow through a pipe is generally characterized as laminar for Re < 2,100, fully turbulent for Re > 10,000, and transitional flow for 2,100 < Re < 10,000.
Hint 2
The Reynolds number for a Newtonian fluid:
$$$Re=\frac{vD}{\nu }$$$
where
$$v$$
is the fluid velocity,
$$D$$
is the pipe diameter or the fluid stream dimension or the characteristic length, and
$$\nu $$
is the kinematic viscosity.
The Reynolds number for a Newtonian fluid:
$$$Re=\frac{vD\rho}{\mu}$$$
where
$$v$$
is the fluid velocity,
$$D$$
is the pipe diameter or the fluid stream dimension or the characteristic length,
$$\rho$$
is the mass density, and
$$\mu$$
is the dynamic viscosity (or absolute viscosity).
$$$Re=\frac{(2ft/s)(0.25ft)(500lb/ft^3)}{0.05\frac{lb}{ft\cdot s}}=\frac{250}{0.05}=5,000$$$
Flow through a pipe is generally characterized as laminar for Re < 2,100, fully turbulent for Re > 10,000, and transitional flow for 2,100 < Re < 10,000.
Since
$$2,100<5,000<10,000$$
, the flow is characterized as transitional.
Transitional
Time Analysis
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