A series of tests in which water was heated while flowing through a 1 m-long electrically heated tube of 1.3 cm ID yielded the experimental pressure-drop data shown next.
GIVEN
Water flowing through a tube
Isothermal and nonisothermal pressure drop data given above
The dimensionless friction factor
Reynolds number
Inside tube diameter
Tube length
FIND
Dimensionless equation of the form:
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 13, for water
The exponent n will be determined from the isothermal data by the least squares fit for log ReD vs. log f
The least squares straight line fit for the data is
The data and straight line fit are shown below
Evaluating ReD (based on the bulk temperature), 0.149 Re–0.1715, f (based on the bulk temperature), and
?s/?f for the non-isothermal case
The linear least square fit for this data is
Therefore: 
The data for x and y and the straight line fit are shown below
Comparing the correlation to the experimental data
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A steel pipe (E 5 190 GPa, ? 5 14 3 1026/°C, d2 5 82 mm) of length L 5 4.25 m hangs from a rigid surface and is subjected to a temperature increase ?T 5 50 °C. The column is fixed at the top and has a small gap at the bottom. To avoid buckling, the minimum clearance at the bottom should be approximately:
(A) 2.55 mm
(B) 3.24 mm
(C) 4.17 mm
(D) 5.23 mm
The absence of liquid water on Venus is responsible for its ________.
A. dense, corrosive atmosphere B. magnetic field C. retrograde rotation D. tall volcanic peaks
Molecules in a region of expanding air more often collide with neighboring molecules that are
A) approaching. B) receding. C) nearly out of range.
Lithosphere
What will be an ideal response?