heating water

Although turbulent flow improves convective heat transfer, it
also increases head loss, and thus requires more pumping
power to maintain a given flow rate relative to the power
required for i29 laminar formulas flow. However, the increased heat
transfer capabilities of turbulent flow often far outweigh
the penalty associated with the increased pumping power.
Thus, when possible, all heat exchangers should be
operated with turbulent ⎛ flow of both fluids.
q = A
k ⎞
⎝
⎜
∆ x ⎠
⎟ (∆T )
REYNOLDS NUMBER
It’s possible to predict if flow through a pipe or across a
smooth plate will be laminar or turbulent. It’s based on
calculating a dimensionless quantity called the Reynolds
number of the fluid (abbreviated as Re#).
q = A R (∆T )
The Reynolds number is a ratio of the inertial forces existing
in a flow stream compared to the viscous forces in that
flow stream. It takes several physical characteristics of
the flowing fluid into account, including the fluid’s density
and viscosity, R both = ∆ x
of which are dependent on the fluid’s
temperature. It also
kaccounts for the speed of the fluid and
the geometry of surfaces in contact with the fluid.
When the Reynolds number is low, the inertial forces
are relatively weak q = hA(∆T compared ) to the viscous forces. Any
disturbance to the flow stream that might otherwise induce
turbulence is quickly dampened out by viscous forces, and
thus sustained turbulence cannot exist. However, when the
inertial forces become dominant over the viscous forces,
which would be characterized by higher Reynolds numbers,
the dampening effects of viscosity are not able to prevent
turbulent flow q from = sAF T 4 4
12 ( − T
1 2 )
being established and maintained.
For flow through a round pipe, the Re# is calculated using
Formula 4-1.
⎣ ⎦
Formula 4-1:
⎡ 1
+ 1 ⎤
⎢ −1⎥
e 1
e 2
Re# = vdD
µ
where:
v = average flow velocity of the ⎛fluid 1 ft (ft/sec) ⎞
d = (0.811 in)
d = internal diameter of pipe (ft)
⎝
⎜
12 in⎠
⎟
D = fluid’s density (lb/ft 3 )
µ = fluid’s dynamic viscosity (lb/ft/sec)
= 0.06758 ft
If the Reynolds number of flow through a round pipe is
over 4,000, the flow will be turbulent. If the Re# is below
⎛
2,300, the flow v = through 0.408 ⎞
the pipe will be laminar. If the Re#
is between 2300 and ⎝
⎜
4000, d 2 ⎠
⎟ f
the flow could be either laminar
or turbulent, and it could switch back and forth.
density (lb/ft3)
Figure 4-3
63
62.5
62
61.5
61
60.5
60
59.5
59
58.5
58
50 100 150 200 250
Here’s an example: Determine the Reynolds number of
water at 140°F flowing at 5 gpm through a 3/4-inch type M
copper tube. Is this flow laminar or turbulent?
Solution: To calculate the Re#, the density and dynamic
viscosity of the water must be determined. The density of
water can be found from Figure 4-3. The dynamic viscosity
of water can be found from Figure 4-4.
Figure 4-4
dynamic viscosity (lb/ft/sec)
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
0
50 100 150 200 250
34
⎛
v = 0.408 ⎞
⎛
⎝
⎜
d 2 ⎠
⎟ f = 0.408
⎜
⎝
⎜ 0.811
( ) 2
⎞
⎟
⎠
⎟
5 = 3.1
ft
sec