Water is flowing in a smooth pipe of diameter D. A section of this pipe having a length of L is…

Water is flowing in a smooth pipe of diameter D. A section
of this pipe having a length of L is heated. Water at the inlet to the heated
section has a temperature of Tf1. Water temperature at the exit of
the heated section is Tf2. The heated section of the pipe wall is
maintained at Ts. Show that for turbulent flow in the pipe and a
specified heated length and pipe diameter, pressure drop in the heated section
is given by:

[Hint: Use Newton’s law of cooling in conjunction with
Equations IIIb.3.6, IIIb.3.7, and IVb.2.20].

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